Dissertations / Theses: 'Montel theorem'

1

Bär, Christian. "Some properties of solutions to weakly hypoelliptic equations." Universität Potsdam, 2012. http://opus.kobv.de/ubp/volltexte/2012/6006/.

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A linear differential operator L is called weakly hypoelliptic if any local solution u of Lu = 0 is smooth. We allow for systems, i.e. the coefficients may be matrices, not necessarily of square size. This is a huge class of important operators which covers all elliptic, overdetermined elliptic, subelliptic and parabolic equations. We extend several classical theorems from complex analysis to solutions of any weakly hypoelliptic equation: the Montel theorem providing convergent subsequences, the Vitali theorem ensuring convergence of a given sequence, and Riemann's first removable singularity theorem. In the case of constant coefficients we show that Liouville's theorem holds, any bounded solution must be constant and any L^p solution must vanish.

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Marchioli, Andresa Baldam [UNESP]. "Dinâmica de endomorfismos do plano complexo e conjuntos de Julia na esfera de Rieman." Universidade Estadual Paulista (UNESP), 2009. http://hdl.handle.net/11449/94261.

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Made available in DSpace on 2014-06-11T19:26:56Z (GMT). No. of bitstreams: 0 Previous issue date: 2009-08-10Bitstream added on 2014-06-13T18:07:02Z : No. of bitstreams: 1 marchioli_ab_me_sjrp.pdf: 317494 bytes, checksum: 518683b62d488d3433a0bee79ecd4f53 (MD5)
Neste trabalho, estudaremos as propriedades dinâmicas de endomorfismos do plano complexo C. Provaremos e o teorema de Montel e mostraremos algumas propriedades topológicas do conjunto de Julia J(f), onde f : C seta C é uma aplicação racional de grau > ou = 2
In this work, we will study the dynamical properties of endomorfisms of complex plane C. We will also prove Montel's theorem and show some topological properties of Julia set J(f), where f : C 'seta' C is a rational map of degree > ou = 2.

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Giner, Emmanuel. "Méthodes d'interaction de configurations et Monte Carlo quantique : marier le meilleur des deux mondes." Toulouse 3, 2014. http://thesesups.ups-tlse.fr/2722/.

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Mes travaux concernent principalement le problème de la corrélation électronique dans les systèmes tels que les atomes ou les molécules. Il sera ici principalement question de méthodes de configuration d'interactions (CI) et de Fixed Node Diffusion Monte Carlo (FN-DMC) appliqués aux calculs de propriétés électroniques telles que l'énergie de corrélation ou les différences d'énergies. L'idée novatrice de ce travail est d'utiliser des fonctions d'ondes CI comme fonctions d'essais pour le FN-DMC, et on montrera que grâce à un algorithme de sélection intelligent de déterminants de Slater, celles ci peuvent en pratique donner d'excellents résultats. On montrera comment on peut améliorer les résultats des méthodes de fonctions d'ondes grâce à la puissance du FN-DMC
This work mainly concerns the general problem of the electronic correlation in molecular and atomic systems. The methods used here to asses this problem belong to two usually separate approaches, namely the configuration interaction (CI) and fixed node diffusion Monte Carlo (FN-DMC). The key idea of this work is to use CI wave functions as trial wave functions for the FN-DMC algorithm, and it will be shown that thanks to wise selection of Slater determinants, these wave function can be used in practice in such context. We will show that the FN-DMC used in this way improve considerably the results obtained with the CI approach

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4

Voegele, Simon. "Shortfall-Minimierung Theorie und Monte Carlo Simulation /." St. Gallen, 2007. http://www.biblio.unisg.ch/org/biblio/edoc.nsf/wwwDisplayIdentifier/02922300001/$FILE/02922300001.pdf.

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5

Fearnhead, Paul. "Sequential Monte Carlo methods in filter theory." Thesis, University of Oxford, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.299043.

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6

Jacob, Alexsandro Machado. "Monte Carlo methods in nonlinear filtering theory." Instituto Tecnológico de Aeronáutica, 2006. http://www.bd.bibl.ita.br/tde_busca/arquivo.php?codArquivo=448.

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This thesis is focused on two basic aspects of the Control Problem: the stochastic modelling of physical systems, and Monte Carlo-based numerical approximation of the nonlinear filtering problem solution. In the first topic this thesis concerns about clarifying some issues in the mathematical modeling of continuous-time systems with Brownian motion. The hypothesis that physical systems should be modelled in continuous-time approach is defended, once the main results in Physics provide solutions for dynamic systems via continuous-time differential equations. It was shown, recalling a main result from the 1960's that a physical system is represented by Fisk-Stratonovich stochastic differential equation, though Ito approach is better to manipulate the mathematical operations. The required conditions for implementing these equations in computers were also studied by using Euler-Maruyama and Milstein schemes of discretization. In the second topic a unified treatment of the available Monte Carlo methods solving the nonlinear filtering problem for continuous and discrete-time modelling is presented with sufficient emphasis on basic applications enabling the engineer to use results provided by the theory. This topic is branched in the study of the theory of nonlinear filtering problem in continuous and discrete-time approaches, and in the investigation of the aspects of Monte Carlo-based numerical solutions approximating unnormalized conditional expectations, as those given by the classical Kallianpur-Striebel formula and its derived robust representation. Investigations showed that the estimates obtained via numerical approximations of the robust representation, or pathwise filter, might accumulate errors when the observation makes this filter alternative equation unstable, a limitation of the method. Another result of this thesis refers to the implementation of Monte Carlo filters using Bayesian representation for discretized models. Although Monte Carlo methods are attractive due to their facility of parallelization, their main drawback is the degeneracy phenomenon of the particles. The traditional resampling scheme solves the problem, but it difficulties the parallelization of the algorithm. The restoration method was then proposed to move the particles towards higher regions in the likelihood function, given information about the model parameters. This open method, in some sense, might decrease the particles degeneracy.

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Ardekani, Armin. "Monte Carlo studies of two dimensional field theories /." Title page, table of contents and introduction only, 1998. http://web4.library.adelaide.edu.au/theses/09PH/09pha676.pdf.

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8

Tuffin, Bruno. "Simulation acceleree par les methodes de monte carlo et quasi-monte carlo : theorie et applications." Rennes 1, 1997. http://www.theses.fr/1997REN10181.

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Dans cette these nous etudions et appliquons les methodes de monte carlo et quasi-monte carlo. Nous nous interessons premierement a la theorie. Les methodes de quasi-monte carlo sont basees sur deux notions : la variation et la discrepance. Comme premiere contribution, nous ameliorons la repartition d'une famille importante de suites a discrepance faible, les suites de halton. Nous realisons ensuite une technique analogue a la reduction de la variance dans les methodes de monte carlo, la reduction de la variation. La borne de l'erreur n'etant que rarement utilisable en pratique, nous proposons une approche pour l'utilisation des suites a discrepance faible comme technique de reduction de la variance dans les methodes de monte carlo. Nous analysons l'efficacite de cette reduction et comparons les differentes suites afin de choisir la mieux adaptee. La deuxieme partie de la these est consacree a des applications concretes et efficaces de ces methodes. Nous considerons d'abord les reseaux de files d'attente multi-classes a forme produit et ameliorons leur simulation par deux techniques differentes de reduction de la variance : les variables antagonistes et les suites a discrepance faible. Cette derniere methode est ensuite appliquee a la simulation d'un systeme cellulaire avec partage dynamique des ressources. Finalement, nous etudions la simulation des systemes markoviens hautement fiables et approfondissons les methodes existantes. Nous introduisons un nouveau concept, l'approximation normale bornee, qui permet d'obtenir une approximation de la loi normale satisfaisante dans le theoreme de la limite centrale, quelle que soit la fiabilite du systeme etudie, et donnons une condition necessaire et suffisante sur la mesure d'echantillonnage preferentiel pour obtenir cette propriete.

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9

Stefancik, John. "Demand forecasting using Monte Carlo Multi-Attribute Utility Theory." Thesis, Massachusetts Institute of Technology, 2016. http://hdl.handle.net/1721.1/104825.

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Thesis: S.M. in Technology and Policy, Massachusetts Institute of Technology, School of Engineering, Institute for Data, Systems, and Society, Technology and Policy Program, 2016.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 173-176).
Volatile commodity prices over the past decade, environmentally-focused policy initiatives and new technology developments have forced manufacturers to consider the idea of substituting towards alternative materials in order meet both consumer and societal needs. The threat of substitution has created the need for manufacturing firms and other members of the supply chain to have the ability to understand the implications of substitution on future product market shares and overall raw material demand. This thesis demonstrates how Multi-Attribute Utility Theory (MAUT) can be extended to the group level to forecast future market shares by applying a distribution to the attribute weights and using a Monte Carlo simulation to capture the choices made by a heterogeneous set of decision makers. Unlike established demand forecasting techniques, such as discrete choice models, this methodology requires only a few data points from a handful of expert interviews and allows for systematic changes of preferences over time. Furthermore, the Monte Carlo MAUT methodology utilizes both revealed preference and stated preference data by integrating the two data types through a response surface methodology. Two case studies on underground distribution and overhead distribution power cables are explored in order to illustrate how the Monte Carlo MAUT methodology can be successfully applied in cases where there are diverse product types, limited numbers of decisions makers and historical market share data is sparse. Each case study illustrates how Monte Carlo MAUT can, on a regional basis, provide key insights into the impacts of changing commodity prices, changing product attribute levels, varying new technology learning rates and changing consumer preferences over time. Furthermore, an example of how Monte Carlo MAUT can be utilized to help policymakers evaluate the advantages, disadvantages and overall impact of different policy schemes within an environmental context is provided. Private firms and public governments alike can utilize Monte Carlo MAUT to improve their understanding of how market shares are likely to change over time, and more importantly, the key decisions needed on each party's behalf in order to maximize societal well-being.
by John Stefancik.
S.M. in Technology and Policy

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10

Jones, Bo. "A New Approximation Scheme for Monte Carlo Applications." Scholarship @ Claremont, 2017. http://scholarship.claremont.edu/cmc_theses/1579.

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Approximation algorithms employing Monte Carlo methods, across application domains, often require as a subroutine the estimation of the mean of a random variable with support on [0,1]. One wishes to estimate this mean to within a user-specified error, using as few samples from the simulated distribution as possible. In the case that the mean being estimated is small, one is then interested in controlling the relative error of the estimate. We introduce a new (epsilon, delta) relative error approximation scheme for [0,1] random variables and provide a comparison of this algorithm's performance to that of an existing approximation scheme, both establishing theoretical bounds on the expected number of samples required by the two algorithms and empirically comparing the samples used when the algorithms are employed for a particular application.

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Allagi, Mabruk Omar F. Mehemed. "Variational processing of Monte Carlo solutions in neutron transport theory." Thesis, University of Cambridge, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.624171.

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12

Amir-Azizi, Siamak. "Linear filtering algorithms for Monte Carlo simulations." Thesis, University of Southampton, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.280859.

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13

Peardon, Michael James. "A study of improved Monte-Carlo methods for lattice gauge theories." Thesis, University of Edinburgh, 1995. http://hdl.handle.net/1842/15616.

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This thesis is concerned with the study and improvement of methods for generating Monte-Carlo configurations used for providing non-perturbative numerical results from lattice gauge theories such as QCD, the theory of strong interactions between quarks and gluons. At present, lattice calculations require large amounts of CPU time on the largest supercomputers. In spite of this numerical assault, the majority of results generated still contain systematic errors from the use of the quenched approximation. In this approximation, employed to dramatically reduce computational costs, the effects of quantum fluctuations in the vacuum of fermion fields are ignored. Chapter 2 investigates the efficiency of a new approximate technique for dynamical fermion simulations which replaces the fermion action with the action of a large number of flavours of locally interacting auxiliary boson fields. The technique is shown to have problematic behaviour in the approach to the limit in which it exactly reproduces the required lattice gauge theory. The autocorrelation time, a measure of efficiency is shown to rise linearly in the number of boson fields employed. Chapter 3 proposes an improvement to this developing method which removes the bias of the approximation introduced. This avoids the computationally difficult approach to the exact limit of the approximation. Chapter 4 involves the calculation of the mass of the scalar glueball of QCD using large lattice spacings to avoid the high penalty for the approach to the continuum limit with an "improved" lattice action to remove the significant discretisation artifacts present at these spacings.

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14

Bohlin, Lars. "Inferens på rangordningar - En Monte Carlo-analys." Thesis, Örebro universitet, Handelshögskolan vid Örebro Universitet, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:oru:diva-46322.

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15

Durmus, Alain. "High dimensional Markov chain Monte Carlo methods : theory, methods and applications." Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLT001/document.

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L'objet de cette thèse est l'analyse fine de méthodes de Monte Carlopar chaînes de Markov (MCMC) et la proposition de méthodologies nouvelles pour échantillonner une mesure de probabilité en grande dimension. Nos travaux s'articulent autour de trois grands sujets.Le premier thème que nous abordons est la convergence de chaînes de Markov en distance de Wasserstein. Nous établissons des bornes explicites de convergence géométrique et sous-géométrique. Nous appliquons ensuite ces résultats à l'étude d'algorithmes MCMC. Nous nous intéressons à une variante de l'algorithme de Metropolis-Langevin ajusté (MALA) pour lequel nous donnons des bornes explicites de convergence. Le deuxième algorithme MCMC que nous analysons est l'algorithme de Crank-Nicolson pré-conditionné, pour lequel nous montrerons une convergence sous-géométrique.Le second objet de cette thèse est l'étude de l'algorithme de Langevin unajusté (ULA). Nous nous intéressons tout d'abord à des bornes explicites en variation totale suivant différentes hypothèses sur le potentiel associé à la distribution cible. Notre étude traite le cas où le pas de discrétisation est maintenu constant mais aussi du cas d'une suite de pas tendant vers 0. Nous prêtons dans cette étude une attention toute particulière à la dépendance de l'algorithme en la dimension de l'espace d'état. Dans le cas où la densité est fortement convexe, nous établissons des bornes de convergence en distance de Wasserstein. Ces bornes nous permettent ensuite de déduire des bornes de convergence en variation totale qui sont plus précises que celles reportées précédemment sous des conditions plus faibles sur le potentiel. Le dernier sujet de cette thèse est l'étude des algorithmes de type Metropolis-Hastings par échelonnage optimal. Tout d'abord, nous étendons le résultat pionnier sur l'échelonnage optimal de l'algorithme de Metropolis à marche aléatoire aux densités cibles dérivables en moyenne Lp pour p ≥ 2. Ensuite, nous proposons de nouveaux algorithmes de type Metropolis-Hastings qui présentent un échelonnage optimal plus avantageux que celui de l'algorithme MALA. Enfin, nous analysons la stabilité et la convergence en variation totale de ces nouveaux algorithmes
The subject of this thesis is the analysis of Markov Chain Monte Carlo (MCMC) methods and the development of new methodologies to sample from a high dimensional distribution. Our work is divided into three main topics. The first problem addressed in this manuscript is the convergence of Markov chains in Wasserstein distance. Geometric and sub-geometric convergence with explicit constants, are derived under appropriate conditions. These results are then applied to thestudy of MCMC algorithms. The first analyzed algorithm is an alternative scheme to the Metropolis Adjusted Langevin algorithm for which explicit geometric convergence bounds are established. The second method is the pre-Conditioned Crank-Nicolson algorithm. It is shown that under mild assumption, the Markov chain associated with thisalgorithm is sub-geometrically ergodic in an appropriated Wasserstein distance. The second topic of this thesis is the study of the Unadjusted Langevin algorithm (ULA). We are first interested in explicit convergence bounds in total variation under different kinds of assumption on the potential associated with the target distribution. In particular, we pay attention to the dependence of the algorithm on the dimension of the state space. The case of fixed step sizes as well as the case of nonincreasing sequences of step sizes are dealt with. When the target density is strongly log-concave, explicit bounds in Wasserstein distance are established. These results are then used to derived new bounds in the total variation distance which improve the one previously derived under weaker conditions on the target density.The last part tackles new optimal scaling results for Metropolis-Hastings type algorithms. First, we extend the pioneer result on the optimal scaling of the random walk Metropolis algorithm to target densities which are differentiable in Lp mean for p ≥ 2. Then, we derive new Metropolis-Hastings type algorithms which have a better optimal scaling compared the MALA algorithm. Finally, the stability and the convergence in total variation of these new algorithms are studied

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16

Xia, Yuan. "Multilevel Monte Carlo for jump processes." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:7bc8e98a-0216-4551-a1f3-1b318e514ee8.

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This thesis consists of two parts. The first part (Chapters 2-4) considers multilevel Monte Carlo for option pricing in finite activity jump-diffusion models. We use a jump-adapted Milstein discretisation for constant rate cases and with the thinning method for bounded state-dependent rate cases. Multilevel Monte Carlo estimators are constructed for Asian, lookback, barrier and digital options. The computational efficiency is numerically demonstrated and analytically justified. The second part (Chapter 5) deals with option pricing problems in exponential Lévy models where the increments of the underlying process can be directly simulated. We discuss several examples: Variance Gamma, Normal Inverse Gaussian and alpha-stable processes and present numerical experiments of multilevel Monte Carlo for Asian, lookback, barrier options, where the running maximum of the Lévy process involved in lookback and barrier payoffs is approximated using discretely monitored maximum. To analytically verify the computational complexity of multilevel method, we also prove some upper bounds on L^p convergence rate of discretely monitored error for a broad class of Lévy processes.

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17

Düchs, Dominik. "Field theories for copolymer blends self consistent approaches and Monte Carlo simulations /." [S.l. : s.n.], 2003. http://deposit.ddb.de/cgi-bin/dokserv?idn=967589339.

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18

Leow, Kai-Siong. "Pricing of swing options| A Monte Carlo simulation approach." Thesis, Kent State University, 2014. http://pqdtopen.proquest.com/#viewpdf?dispub=3618875.

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We study the problem of pricing swing options, a class of multiple early exercise options that are traded in energy market, particularly in the electricity and natural gas markets. These contracts permit the option holder to periodically exercise the right to trade a variable amount of energy with a counterparty, subject to local volumetric constraints. In addition, the total amount of energy traded from settlement to expiration with the counterparty is restricted by a global volumetric constraint. Violation of this global volumetric constraint is allowed but would lead to penalty settled at expiration.

The pricing problem is formulated as a stochastic optimal control problem in discrete time and state space. We present a stochastic dynamic programming algorithm which is based on piecewise linear concave approximation of value functions. This algorithm yields the value of the swing option under the assumption that the optimal exercise policy is applied by the option holder. We present a proof of an almost sure convergence that the algorithm generates the optimal exercise strategy as the number of iterations approaches to infinity. Finally, we provide a numerical example for pricing a natural gas swing call option.

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19

Leino, Anders. "Exact and Monte-Carlo algorithms for combinatorial games." Thesis, Umeå universitet, Institutionen för fysik, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-88363.

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This thesis concerns combinatorial games and algorithms that can be used to play them.Basic definitions and results about combinatorial games are covered, and an implementation of the minimax algorithm with alpha-beta pruning is presented.Following this, we give a description and implementation of the common UCT (Upper Confidence bounds applied to Trees) variant of MCTS (Monte-Carlo tree search).Then, a framework for testing the behavior of UCT as first player, at various numbers of iterations (namely 2,7, ... 27), versus minimax as second player, is described.Finally, we present the results obtained by applying this framework to the 2.2 million smallest non-trivial positional games having winning sets of size either 2 or 3.It is seen that on almost all different classifications of the games studied, UCT converges quickly to near-perfect play.
Denna rapport handlar om kombinatoriska spel och algoritmer som kan användas för att spela dessa.Grundläggande definitioner och resultat som berör kombinatoriska spel täcks, och en implementation av minimax-algoritmen med alpha-beta beskärning ges.Detta följs av en beskrivning samt en implementation av UCT varianten av MCTS (Monte-Carlo tree search).Sedan beskrivs ett ramverk för att testa beteendet för UCT som första spelare, vid olika antal iterationer (nämligen 2, 7, ... 27), mot minimax som andra spelare.Till sist beskrivs resultaten vi funnit genom att använda detta ramverk för att spela de 2,2 miljoner minsta icke triviala positionella spelen med vinstmängder av storlek antingen 2 eller 3.Vi finner att, för nästan alla olika klassificeringar av spel vi studerar, så konvergerar UCT snabbt mot nära perfekt spel.

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20

Livingstone, S. J. "Some contributions to the theory and methodology of Markov chain Monte Carlo." Thesis, University College London (University of London), 2016. http://discovery.ucl.ac.uk/1473910/.

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The general theme of this thesis is developing a better understanding of some Markov chain Monte Carlo methods. We review the literature in Chapters 1-4, including a short discussion of geometry in Markov chain Monte Carlo. In Chapter 5 we consider Langevin diffusions. First, a new class of these are derived in which the volatility is made position-dependent, using tools from stochastic analysis. Second, a complementary derivation is given, here using tools from Riemannian geometry. We hope that this work will help develop understanding of the geometric perspective among statisticians. Such derivations have been attempted previously, but solutions were not correct in general. We highlight these issues in detail. In the final part discussion is given on the use of these objects in Markov chain Monte Carlo. In Chapter 6 we consider a Metropolis-Hastings method with proposal kernel N(x,hV(x)), where x is the current state. After reviewing instances in the literature, we analyse the ergodicity properties of the resulting Markov chains. In one dimension we find that suitable choice of V(x) can change these compared to the Random Walk Metropolis case N(x,hS), for better or worse. In higher dimensions we show that judicious choice of V(x) can produce a geometrically converging chain when probability concentrates on an ever narrower ridge as |x| grows, something which is not true for the Random Walk Metropolis. In Chapter 7 we discuss stability of Hamiltonian Monte Carlo. For a fixed integration time we establish conditions for irreducibility and geometric ergodicity. Some results are confined to one dimension, and some further to a reference class of distributions. We find that target distributions with tails that are in between Exponential and Gaussian are needed for geometric ergodicity. Next we consider changing integration times, and show that here a geometrically ergodic chain can be constructed when tails are heavier than Exponential.

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21

Graham, Matthew McKenzie. "Auxiliary variable Markov chain Monte Carlo methods." Thesis, University of Edinburgh, 2018. http://hdl.handle.net/1842/28962.

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Markov chain Monte Carlo (MCMC) methods are a widely applicable class of algorithms for estimating integrals in statistical inference problems. A common approach in MCMC methods is to introduce additional auxiliary variables into the Markov chain state and perform transitions in the joint space of target and auxiliary variables. In this thesis we consider novel methods for using auxiliary variables within MCMC methods to allow approximate inference in otherwise intractable models and to improve sampling performance in models exhibiting challenging properties such as multimodality. We first consider the pseudo-marginal framework. This extends the Metropolis–Hastings algorithm to cases where we only have access to an unbiased estimator of the density of target distribution. The resulting chains can sometimes show ‘sticking’ behaviour where long series of proposed updates are rejected. Further the algorithms can be difficult to tune and it is not immediately clear how to generalise the approach to alternative transition operators. We show that if the auxiliary variables used in the density estimator are included in the chain state it is possible to use new transition operators such as those based on slice-sampling algorithms within a pseudo-marginal setting. This auxiliary pseudo-marginal approach leads to easier to tune methods and is often able to improve sampling efficiency over existing approaches. As a second contribution we consider inference in probabilistic models defined via a generative process with the probability density of the outputs of this process only implicitly defined. The approximate Bayesian computation (ABC) framework allows inference in such models when conditioning on the values of observed model variables by making the approximation that generated observed variables are ‘close’ rather than exactly equal to observed data. Although making the inference problem more tractable, the approximation error introduced in ABC methods can be difficult to quantify and standard algorithms tend to perform poorly when conditioning on high dimensional observations. This often requires further approximation by reducing the observations to lower dimensional summary statistics. We show how including all of the random variables used in generating model outputs as auxiliary variables in a Markov chain state can allow the use of more efficient and robust MCMC methods such as slice sampling and Hamiltonian Monte Carlo (HMC) within an ABC framework. In some cases this can allow inference when conditioning on the full set of observed values when standard ABC methods require reduction to lower dimensional summaries for tractability. Further we introduce a novel constrained HMC method for performing inference in a restricted class of differentiable generative models which allows conditioning the generated observed variables to be arbitrarily close to observed data while maintaining computational tractability. As a final topicwe consider the use of an auxiliary temperature variable in MCMC methods to improve exploration of multimodal target densities and allow estimation of normalising constants. Existing approaches such as simulated tempering and annealed importance sampling use temperature variables which take on only a discrete set of values. The performance of these methods can be sensitive to the number and spacing of the temperature values used, and the discrete nature of the temperature variable prevents the use of gradient-based methods such as HMC to update the temperature alongside the target variables. We introduce new MCMC methods which instead use a continuous temperature variable. This both removes the need to tune the choice of discrete temperature values and allows the temperature variable to be updated jointly with the target variables within a HMC method.

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22

Kim, Jae-Kwon. "Monte-Carlo simulation study of problems of quantum field theory and critical phenomena." Diss., The University of Arizona, 1992. http://hdl.handle.net/10150/185853.

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In chapter one, we explain briefly the continuum limit, scaling, and high temperature expansion of critical phenomena, Monte Carlo algorithms and fitting. In chapter two, different continuum limits of the Ising model in dimensions (D) 2, 3 and 4 are investigated numerically. The data indicate that triviality occurs for D = 4 and fails for D < 4 in each limit. In chapter three, a relation between the critical exponents of the leading and confluent scaling terms is derived using the finite size scaling argument. We also determine the new scaling variable of the 4D Ising model based on a new Monte Carlo simulation data. In chapter four, a Monte Carlo study of two dimensional diluted Ising systems is reported. It is shown that regular dilution does not affect critical exponents, while a random one does, with critical exponents varying continuously with impurity concentration. The importance of fluctuations in producing such effects is emphasized. In chapter five, a different point of view regarding the critical exponent of the specific heat of the 3D Ising model is presented. Based on the analysis of high temperature expansion, finite size scaling and Monte Carlo data in the symmetric phase of the 3D Ising model, it is shown that logarithmic scaling behavior of specific heat is more consistent than power scaling behavior.

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23

Wüst, Thomas. "Growth-induced polarity formation in molecular crystals : analytical theory and Monte Carlo simulations /." [S.l.] : [s.n.], 2005. http://www.zb.unibe.ch/download/eldiss/05wuest_t.pdf.

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24

Rangaraj, Dharanipathy. "Multicomponent aerosol dynamics : exploration of direct simulation Monte Carlo technique /." free to MU campus, to others for purchase, 2004. http://wwwlib.umi.com/cr/mo/fullcit?p3144452.

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25

Widman, Linnea. "Från det imaginära till normala familjer : Analytiska konvergenser." Thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-59771.

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I komplex analys finns det ett antal olika konvergenser varav vi tittar närmare på några här. Bland annat hur likformig konvergens medför punktvis konvergens men att det omvända ej gäller. Vi tittar också på vad de har för samband med lokal likformig konvergens och normal konvergens dvs. likformig konvergens på kompakta delmängder. Slutligen kommer vi att se på vad som gäller för familjer och kommer då in på lokalt begränsad, ekvikontinuitet, Arzela/Ascoli, Montels och Runges satser. Vi kommer här även se exempel på hur stort fel det egentligen kan bli för punktvisa konvergenta följder. De får normalt inte en gränsfunktion som är analytisk men vi ser både i Exempel 3.19 och Korollarium 3.23 att dessa ger resultat som är analytiska nästan överallt.
This report will describe four different types of convergence. The types described are pointwise, local uniformly, uniformly and normal convergence. The different convergences are explored in a way of how they relate to each other. Finally this report will also investigate how this applies to normal families and the theories of Arzela/Ascoli, Montel and Runge. We will here see examples of how wrong it really can go for pointwise convergent sequences. They do usually not have a limit that is analytic but from both Example 3.19 and Corollary 3.23 we will see that they give functions that in fact are analytic almost everywhere.

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De, Joannis Jason. "Equilibrium properties of polymer solutions at surfaces Monte Carlo simulations /." [Florida] : State University System of Florida, 2000. http://etd.fcla.edu/etd/uf/2000/ane5947/dissertation%5Fdone.pdf.

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Thesis (Ph. D.)--University of Florida, 2000.
Title from first page of PDF file. Document formatted into pages; contains ix, 242 p.; also contains graphics. Vita. Includes bibliographical references (p. 232-241).

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Lang, Gladys Hau-Wan Goddard William A. Koonin Steven E. "Auxiliary-field Monte Carlo methods for interacting fermions application to the nuclear shell model /." Diss., Pasadena, Calif. : California Institute of Technology, 1993. http://resolver.caltech.edu/CaltechTHESIS:10222009-160215418.

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Thesis (Ph. D.)--California Institute of Technology, 1993. UM #93-25,365.
Advisor names found in the Acknowledgments pages of the thesis. Title from home page. Viewed 01/22/2010. Includes bibliographical references.

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28

Wigren, Anna. "Exploiting conjugacy in state-space models with sequential Monte Carlo." Licentiate thesis, Uppsala universitet, Avdelningen för systemteknik, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-429236.

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Many processes we encounter in our daily lives are dynamical systems that can be described mathematically using state-space models. Exact inference of both states and parameters in these models is, in general, intractable. Instead, approximate methods, such as sequential Monte Carlo and Markov chain Monte Carlo, are used to infer quantities of interest. However, sample based inference inherently introduce variance in the estimates. In this thesis we explore different aspects of how conjugacy relations in a model can improve the performance of sequential Monte Carlo-based inference methods.A conjugacy relation between the prior distribution and the likelihood implies that the posterior distribution has the same distributional form as the prior, allowing for analytic updates in place of numerical integration. In Paper I we consider state inference in state-space models where the transition density is intractable. By adding artificial noise conjugate to the observation density we can design an efficient proposal for sequential Monte Carlo inference that can reduce the variance of the state estimates. Conjugacy can also be utilized in the setting of parameter inference. In Paper II we show that the performance of particle Gibbs-type samplers, in terms of the autocorrelation of the samples, can be improved when conjugacy relations allow for marginalizing out the dependence on parameters in the state update.Despite enabling analytical evaluation of integrals, the derivation and implementation of conjugacy updates is cumbersome in all but the simplest cases, which limits the usefulness in practice. Recently, the emerging field of probabilistic programming has changed this, by providing a framework for automating inference in probabilistic models - including identifying and utilizing conjugacy relations. In Paper II we make use of probabilistic programming to automatically exploit conjugacy in an epidemiological state-space model describing the spread of dengue fever.

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SMITH, WARREN ESCHHOLZ. "SIMULATED ANNEALING AND ESTIMATION THEORY IN CODED-APERTURE IMAGING (RECONSTRUCTION, MONTE CARLO, WIENER FILTER)." Diss., The University of Arizona, 1985. http://hdl.handle.net/10150/188135.

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Coded-aperture imaging without detector motion can be used to reconstruct three-dimensional radionuclide distributions in the context of nuclear medicine. This approach offers several advantages over the rotating gamma-ray camera systems presently employed in the clinic. These advantages include improved sensitivity, potentially better spatial resolution, and the capability of doing dynamic studies. There are two problems associated with the coded-aperture approach, however. First, the data is "multiplexed", which refers to the fact that many line integrals of the source distribution are combined together and not measured individually, so that information is lost. Second, the number of resolvable detector elements is typically an order of magnitude less than the number of object elements to be reconstructed, so that the reconstruction problem is underdetermined. Consequently, the reconstruction is not unique. By using various types of a priori information in forming the reconstruction, however, it is possible to augment the incomplete data set. Two algorithms are presented to reconstruct objects from their coded-image projections and various types of a priori information. The first, a Monte Carlo algorithm, is a flexible and computationally efficient approach using the a priori knowledge of positivity and nearest-neighbor correlation. This algorithm is used to qualitatively explore the effect of the data-taking geometry on reconstruction performance. The second algorithm is a linear estimator incorporating as a priori knowledge completely general first- and second-order statistical information about the object class to be reconstructed. The linear-estimator formalism also provides a minimum-variance expression for system optimization. This linear algorithm is used to explore the effects of correct and incorrect a priori information on reconstruction performance, and to quantitatively investigate reconstruction quality with respect to data-taking geometry.

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Korotana, Romi Kaur. "A combined density functional theory and Monte Carlo study of manganites for magnetic refrigeration." Thesis, Imperial College London, 2014. http://hdl.handle.net/10044/1/42887.

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Perovskite oxides such as manganites are considered to be strong candidates for appli- cations in magnetic refrigeration technology, due to their remarkable magnetocaloric properties, in addition to low processing costs. Manganites with the general formula R1-x AxMnO3, particularly for A=Ca and 0.2 < x < 0.5, undergo a field driven tran- sition from a paramagnetic to ferromagnetic state, which is accompanied by changes in the lattice and electronic structure. Therefore, one may anticipate a large entropy change across the phase transition due to the first order nature. Despite many ex- perimental efforts to enhance the isothermal entropy change in manganites, the max- imum obtained value merely reaches a modest value in the field of a permanent mag- net. The present work aims to achieve an understanding of the relevant structural, magnetic, and electronic energy contributions to the stability of the doped compound La0.75Ca0.25MnO3 . A combination of thermodynamics and first principles theory is applied to determine individual contributions to the total entropy change of the system by treating the electronic, lattice and magnetic components independently. For this purpose, hybrid-exchange density functional (B3LYP) calculations are performed for LaMnO3, CaMnO3 and La0.75Ca0.25MnO3 . The most stable phases for the end-point compounds are described correctly. Computed results for the doped compound predict an anti-Jahn-Teller polaron in the localised hole state, which is influenced by long- range cooperative Jahn-Teller distortions. The analysis of the energy scales related to the magnetocaloric effect suggests that the charge, orbital, spin and lattice degrees of freedom are strongly coupled, since they are of a similar magnitude. Through the analysis of individual entropy contributions, it is identified that the electronic and lat- tice entropy changes oppose the magnetic entropy change. Therefore, the electronic and vibrational terms have a deleterious effect on the total entropy change. The results highlighted in the present work may provide a useful framework for the interpretation of experimental observations as well as valuable guidelines for tuning the magnetocaloric properties of oxides, such as manganites.

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Lin, Haiping. "Simulations of chiral ordering of achiral molecules by Density Functional Theory and Monte Carlo." Thesis, University of Liverpool, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.490915.

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The self-organization of organic molecules on metal surfaces can play a crucial role in various subjects of science such as electrochemistry and heterogeneous catalysis. However, their practical applications have been suffering from lack of atomic scale understanding of the ordering behavior. Theoretically, however, the description of the self-assembly processes has been limited by the inability of microscopic models to account for the interplay of all elementary processes at realistic temperatures and pressures. In this work, we take the succinate molecules and Cu(1IO) surface as a model system to study the nature of the asymmetric self-assembly behavior of the achiral adsorbates on an achiral surface. In the first step, density-functional theory (DFT) is used to accurately characterize the molecule-surface system on the microscopic level. The obtained energetics is then employed to parameterize a lattice gas Hamiltonian, which subsequently allows to address the mesoscopic ordering behavior at finite temperatures by means of ~v1onte Carlo simulations. Two well-defined ordered structures have appeared in the rvlonte Carlo simulations. The (5 0, 3 2) structure has been confirmed to be the ground state configuration by direct DFT calculations. This structure has not been reported before and it can be the ordering configuration observed in some STrvI experiments. By summing up all the calculations, the nature of the self-organization behavior of succinate molecules on Cu(llO) is attributed to the indirect lateral interactions of the adsorbates. This result may provide a new understanding of designing two dimensional periodic architectures on metal surfaces. Supplied by The British Library - 'The world's knowledge'

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Subramanian, Ramachandran. "Quantum virial coefficients via path integral Monte Carlo| Theory and development of novel algorithms." Thesis, State University of New York at Buffalo, 2016. http://pqdtopen.proquest.com/#viewpdf?dispub=10127734.

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Virial coefficients are unique thermodynamic properties of a system owing to their link be- tween interactions at the molecular level to macroscopic quantities such as the pressure. In this work, we take advantage of this feature and compute virial coefficients of a variety of systems by performing simulation studies. The nature and quality of the interaction potential used in such studies highly affects the quality of the resulting virial coefficients. Therefore, we have employed ab initio based interaction potentials that are state-of-the-art and have been developed using high quality quantum chemistry calculations. Naturally, the complexity of such simulations is a strong motivator for the development of algorithms that are highly efficient and yield precise results. In this regard, we have developed two efficient and novel algorithms for use in Path Integral Monte Carlo (PIMC), a method used to incorporate nuclear quantum effects in virial coefficient calculations for diatomic molecules. We have successfully applied these algorithms to compute virial coefficients including quantum effects or, in short, quantum virial coefficients, for H₂, N₂ and O₂ sys- tems. In addition to applying these algorithms to study diatomic molecules, we have also investigated other algorithms like PIMC using semi-classical beads and compared them to conventional PIMC, for He as well as N₂ systems. Finally, we have also evaluated virial coefficients including quantum corrections, or, in short, semi-classical virial coefficients for a latest ab initio potential of water.

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Obodi, G. N. "Monte Carlo studies of gε⁴ scaler field and the Abelian-Higgs theories in 3-dimensions." Thesis, Imperial College London, 1985. http://hdl.handle.net/10044/1/37805.

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Shi, Feng. "Nucleation and growth in materials and on surfaces : kinetic Monte Carlo simulations and rate equation theory /." Connect to full text in OhioLINK ETD Center, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1216839589.

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35

Schöön, Jonathan. "Pricing Put Options with Multilevel Monte Carlo Simulation." Thesis, Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-55404.

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Monte Carlo path simulations are common in mathematical and computational finance as a way of estimating the expected values of a quantity such as a European put option, which is functional to the solution of a stochastic differential equation (SDE). The computational complexity of the standard Monte Carlo (MC) method grows quite large quickly, so in this thesis we focus on the Multilevel Monte Carlo (MLMC) method by Giles, which uses multigrid ideas to reduce the computational complexity. We use a Euler-Maruyama time discretisation for the approximation of the SDE and investigate how the convergence rate of the MLMC method improves the computational times and cost in comparison with the standard MC method. We perform a numerical analysis on the computational times and costs in order to achieve the desired accuracy and present our findings on the performance of the MLMC method on a European put option compared to the standard MC method.

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Higdon, David. "Spatial applications of Markov chain Monte Carlo for Bayesian inference /." Thesis, Connect to this title online; UW restricted, 1994. http://hdl.handle.net/1773/8942.

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37

Pownall, Christopher David. "Simulation and theory of island growth on stepped substrates." Thesis, University of Reading, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.298745.

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38

Shi, Feng. "Nucleation and Growth in Materials and on Surfaces:Kinetic Monte Carlo Simulation and Rate Equation Theory." University of Toledo / OhioLINK, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1216839589.

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39

Peil, Oleg E. "Theory of Disordered Magnets." Doctoral thesis, Uppsala universitet, Institutionen för fysik och materialvetenskap, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-9528.

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Studying magnetic properties of disordered alloys is important both for the understanding of phase transformations in alloys and from the point of view of fundamental issues of magnetism in solids. Disorder in a magnetic system can result in unconventional magnetic structures, such as spin glass, which have rather peculiar features. In this Thesis, a rather general approach to studying disordered magnetic alloys from first principles is presented. Phase transformations and magnetic behavior of crystalline substitutional alloys are considered. This approach is exemplified by calculations of an archetypical spin-glass material: the CuMn alloy. First, a general theoretical framework for the description of the thermodynamics of disordered magnetic alloys is given. It is shown that under certain conditions, a complex magnetic system can be reduced to an effective system containing no magnetic degrees of freedom. This substantially simplifies the investigation of phase transformations in magnetic alloys. The effective model is described in terms of material-specific interaction parameters. It is shown that interaction parameters can be obtained from the ground-state property of a disordered alloy which are in turn calculated from first principles by means of highly accurate up-to-date numerical techniques based on the Green's function method. The interaction parameters can subsequently be used in thermodynamic Monte-Carlo simulations to produce the atomic and magnetic structures of an alloy. An example of calculations for the Cu-rich CuMn alloy is given. It is demonstrated that the atomic and magnetic structure of the alloy obtained by the presented approach agrees very well with the results of neutron-scattering experiments for this system. Moreover, numerical simulations enable one to predict the ground state structure of the alloy, which is difficult to observe in experiment due to large atomic diffusion barriers at temperatures close to the temperature of the phase transformation. A general description of a spin glass is given, and difficulties of modeling this type of magnetic systems are discussed. To overcome the difficulties, improved Monte-Carlo methods, such as parallel tempering, overrelaxation technique, and finite-size scaling method of analysis, are introduced. The results for the CuMn alloy are presented.

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40

Suzuki, Jiro, Atsushi Takano, Tetsuo Deguchi, and Yushu Matsushita. "Dimension of ring polymers in bulk studied by Monte-Carlo simulation and self-consistent theory." American Institute of Physics, 2009. http://hdl.handle.net/2237/14168.

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41

Blackwell, Ruth. "Kinetic Monte Carlo and density fuctional theory applied to heterogeneously catalysed reactions having complex mechanisms." Thesis, Imperial College London, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.512071.

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42

Bramstång, Philip, and Richard Hermanson. "Extreme value theory with Markov chain Monte Carlo - an automated process for EVT in finance." Thesis, KTH, Matematisk statistik, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-172970.

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The purpose of this thesis was to create an automated procedure for estimating financial risk using extreme value theory (EVT). The "peaks over threshold" (POT) result from EVT was chosen for modelling the tails of the distribution of financial returns. The main difficulty with POT is choosing a convergence threshold above which the data points are regarded as extreme events and modelled using a limit distribution. It was investigated how risk measures are affected by variations in this threshold and it was deemed that fixed-threshold models are inadequate in the context of few relevant data points, as is often the case in EVT applications. A model for automatic threshold weighting was proposed and shows promise. Moreover, the choice of Bayesian vs frequentist inference, with focus on Markov chain Monte Carlo (MCMC) vs maximum likelihood estimation (MLE), was investigated with regards to EVT applications, favoring Bayesian inference and MCMC. Two MCMC algorithms, independence Metropolis (IM) and automated factor slice sampler (AFSS), were analyzed and improved in order to increase performance of the final procedure. Lastly, the effects of a reference prior and a prior based on expert opinion were compared and exemplified for practical applications in finance.
Syftet med detta examensarbete var att utveckla en automatisk process för uppskattning av finansiell risk med hjälp av extremvärdesteori. "Peaks over threshold" (POT) valdes som metod för att modellera extrempunkter i avkastningsdata. Den stora svårigheten med POT är att välja ett tröskelvärde för konvergens, över vilket alla datapunkter betraktas som extrema och modelleras med en gränsvärdesdistribution. Detta tröskelvärdes påverkan på olika riskmått undersöktes, med slutsatsen att modeller med fast tröskelvärde är olämpliga om datamängden är liten, vilket ofta är fallet i tillämpade extremvärdesmetoder.En modell för viktning av tröskelvärden presenterades och uppvisade lovande resultat. Därtill undersöktes valet mellan Bayesiansk och frekventisk inferens, med fokus på skillnaden mellan Markov chain Monte Carlo (MCMC) och maximum likelihood estimation (MLE), när det kommer till applicerad extremvärdesteori. Bayesiansk inferens och MCMC bedömdes vara bättre, och två MCMC-algoritmer; independence Metropolis (IM) och automated factor slice sampler (AFSS), analyserades och förbättrades för använding i den automatiska processen. Avslutningsvis jämfördes effekterna av olika apriori sannolikhetsfördelningar (priors) på processens slutresultat. En svagt informativ referensprior jämfördes med en starkt informativ prior baserad på expertutlåtanden.

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Driver, Kevin P. "Establishing Quantum Monte Carlo and Hybrid Density Functional Theory as Benchmarking Tools for Complex Solids." The Ohio State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=osu1296636949.

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44

Damian, Doris. "A Bayesian approach to estimating heterogeneous spatial covariances /." Thesis, Connect to this title online; UW restricted, 2002. http://hdl.handle.net/1773/9563.

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45

Newton, Michael A. "The weighted likelihood bootstrap and an algorithm for prepivoting /." Thesis, Connect to this title online; UW restricted, 1991. http://hdl.handle.net/1773/8962.

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46

Byers, Simon. "Bayesian modeling of highly structured systems using Markov chain Monte Carlo /." Thesis, Connect to this title online; UW restricted, 1998. http://hdl.handle.net/1773/8980.

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47

Scardovi, Elena. "Jarrow-Yildirim model for inflation: theory and applications." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2011. http://amslaurea.unibo.it/2289/.

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This thesis deals with inflation theory, focussing on the model of Jarrow & Yildirim, which is nowadays used when pricing inflation derivatives. After recalling main results about short and forward interest rate models, the dynamics of the main components of the market are derived. Then the most important inflation-indexed derivatives are explained (zero coupon swap, year-on-year, cap and floor), and their pricing proceeding is shown step by step. Calibration is explained and performed with a common method and an heuristic and non standard one. The model is enriched with credit risk, too, which allows to take into account the possibility of bankrupt of the counterparty of a contract. In this context, the general method of pricing is derived, with the introduction of defaultable zero-coupon bonds, and the Monte Carlo method is treated in detailed and used to price a concrete example of contract. Appendixes: A: martingale measures, Girsanov's theorem and the change of numeraire. B: some aspects of the theory of Stochastic Differential Equations; in particular, the solution for linear EDSs, and the Feynman-Kac Theorem, which shows the connection between EDSs and Partial Differential Equations. C: some useful results about normal distribution.

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48

Schwarz, Lauretta Rebecca. "Projector Quantum Monte Carlo methods for linear and non-linear wavefunction ansatzes." Thesis, University of Cambridge, 2017. https://www.repository.cam.ac.uk/handle/1810/267871.

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This thesis is concerned with the development of a Projector Quantum Monte Carlo method for non-linear wavefunction ansatzes and its application to strongly correlated materials. This new approach is partially inspired by a prior application of the Full Configuration Interaction Quantum Monte Carlo (FCIQMC) method to the three-band (p-d) Hubbard model. Through repeated stochastic application of a projector FCIQMC projects out a stochastic description of the Full Configuration Interaction (FCI) ground state wavefunction, a linear combination of Slater determinants spanning the full Hilbert space. The study of the p-d Hubbard model demonstrates that the nature of this FCI expansion is profoundly affected by the choice of single-particle basis. In a counterintuitive manner, the effectiveness of a one-particle basis to produce a sparse, compact and rapidly converging FCI expansion is not necessarily paralleled by its ability to describe the physics of the system within a single determinant. The results suggest that with an appropriate basis, single-reference quantum chemical approaches may be able to describe many-body wavefunctions of strongly correlated materials. Furthermore, this thesis presents a reformulation of the projected imaginary time evolution of FCIQMC as a Lagrangian minimisation. This naturally allows for the optimisation of polynomial complex wavefunction ansatzes with a polynomial rather than exponential scaling with system size. The proposed approach blurs the line between traditional Variational and Projector Quantum Monte Carlo approaches whilst involving developments from the field of deep-learning neural networks which can be expressed as a modification of the projector. The ability of the developed approach to sample and optimise arbitrary non-linear wavefunctions is demonstrated with several classes of Tensor Network States all of which involve controlled approximations but still retain systematic improvability towards exactness. Thus, by applying the method to strongly-correlated Hubbard models, as well as ab-initio systems, including a fully periodic ab-initio graphene sheet, many-body wavefunctions and their one- and two-body static properties are obtained. The proposed approach can handle and simultaneously optimise large numbers of variational parameters, greatly exceeding those of alternative Variational Monte Carlo approaches.

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Edström, Filip. "Parametrization of Reactive Force Field using Metropolis Monte Carlo." Thesis, Umeå universitet, Institutionen för fysik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-161972.

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50

Zöllner, Dana [Verfasser]. "Monte Carlo Potts Model Simulation and Statistical Mean-Field Theory of Normal Grain Growth / Dana Zöllner." Aachen : Shaker, 2006. http://d-nb.info/1166514811/34.

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Dissertations / Theses on the topic 'Montel theorem'

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