Journal articles: 'Processus de Jacobi'

1

Gruet, Jean-Claude. "Jacobi radial stable processes." Annales mathématiques Blaise Pascal 5, no. 2 (1998): 39–48. http://dx.doi.org/10.5802/ambp.109.

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Dung, Nguyen Tien. "JACOBI PROCESSES DRIVEN BY FRACTIONAL BROWNIAN MOTION." Taiwanese Journal of Mathematics 18, no. 3 (May 2014): 835–48. http://dx.doi.org/10.11650/tjm.18.2014.3288.

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3

Ежова, Н. А., and Л. Б. Соколинский. "Scalability evaluation of iterative algorithms for supercomputer simulation of physical processes." Numerical Methods and Programming (Vychislitel'nye Metody i Programmirovanie), no. 4 (December 18, 2018): 416–30. http://dx.doi.org/10.26089/nummet.v19r437.

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Статья посвящена разработке методики исследования масштабируемости ресурсоемких итерационных алгоритмов, применяемых в моделировании сложных физических процессов на суперкомпьютерных системах. В основе предлагаемой методики лежит модель параллельных вычислений BSF (Bulk Synchronous Farm), позволяющая на ранней стадии разработки итерационного алгоритма определить границу его масштабируемости. Модель BSF предполагает представление алгоритма в виде операций над списками с использованием функций высшего порядка. При этом рассматривается два класса представлений: BSF-M (Map BSF) и BSF-MR (Map-Reduce BSF). Предлагаемая методика описывается на примере решения систем линейных алгебраических уравнений методом Якоби. Для метода Якоби строится два итерационных алгоритма: Jacobi-M на основе представления BSF-M и Jacobi-MR на основе представления BSF-MR. Для указанных алгоритмов с помощью стоимостных метрик модели BSF даются аналитические оценки для ускорения, эффективности распараллеливания и верхней границы масштабируемости для многопроцессорных вычислительных систем с распределенной памятью. Приводится информация о реализации этих алгоритмов на языке C++ с использованием программного шаблона BSF и библиотеки параллельного программирования MPI. Демонстрируются результаты масштабных вычислительных экспериментов, выполненных на кластерной вычислительной системе. На основе экспериментальных результатов дается анализ адекватности оценок, полученных аналитическим путем с помощью стоимостных метрик модели BSF. This paper is devoted to the development of a methodology for evaluating the scalability of compute-intensive iterative algorithms used for simulating complex physical processes on supercomputer systems. The proposed methodology is based on the BSF (Bulk Synchronous Farm) parallel computation model, which makes it possible to predict the upper scalability bound of an iterative algorithm in early stages of its design. The BSF model assumes the representation of the algorithm in the form of operations on lists using high-order functions. Two classes of representations are considered: BSF-M (Map BSF) and BSF-MR (Map-Reduce BSF). The proposed methodology is described by the example of solving a system of linear equations by the Jacobi method. For the Jacobi method, two iterative algorithms are constructed: Jacobi-M based on the BSF-M representation and Jacobi-MR based on the BSF-MR representation. Analytical estimations of the speedup, parallel efficiency and upper scalability bound are obtained for these algorithms using the BSF cost metrics on multi-processor computing systems with distributed memory. These algorithms are implemented on C++ language using the BSF program skeleton and MPI parallel programming library. The results of large-scale computational experiments performed on a cluster computing system are discussed. Based on the experimental results, an analysis of the adequacy of estimations obtained analytically using the BSF cost metric is made.

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4

CHOU, C. I., and C. L. HO. "GENERALIZED RAYLEIGH AND JACOBI PROCESSES AND EXCEPTIONAL ORTHOGONAL POLYNOMIALS." International Journal of Modern Physics B 27, no. 24 (September 11, 2013): 1350135. http://dx.doi.org/10.1142/s021797921350135x.

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We present four types of infinitely many exactly solvable Fokker–Planck equations, which are related to the newly discovered exceptional orthogonal polynomials. They represent the deformed versions of the Rayleigh process and the Jacobi process.

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Fink, Holger, and Georg Schlüchtermann. "Fractional Lévy Cox–Ingersoll–Ross and Jacobi processes." Statistics & Probability Letters 142 (November 2018): 84–91. http://dx.doi.org/10.1016/j.spl.2018.07.004.

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6

Gorin, Vadim, and Lingfu Zhang. "Interlacing adjacent levels of $$\beta $$–Jacobi corners processes." Probability Theory and Related Fields 172, no. 3-4 (January 4, 2018): 915–81. http://dx.doi.org/10.1007/s00440-017-0823-8.

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7

Hari, V. "On the convergence of cyclic Jacobi-like processes." Linear Algebra and its Applications 81 (September 1986): 105–27. http://dx.doi.org/10.1016/0024-3795(86)90252-1.

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8

Tang, Bo, Yingzhe Fan, Jixiu Wang, and Shijun Chen. "Exact Solutions for N-Coupled Nonlinear Schrödinger Equations With Variable Coefficients." Zeitschrift für Naturforschung A 71, no. 7 (July 1, 2016): 665–72. http://dx.doi.org/10.1515/zna-2016-0128.

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AbstractIn this paper, based on similarity transformation and auxiliary equation method, we construct many exact solutions ofN-coupled nonlinear Schrödinger equations with variable coefficients, which include soliton solutions, combined soliton solutions, triangular periodic solutions, Jacobi elliptic function solutions and combined Jacobi elliptic function solutions. These solutions may give insight into many considerable physical processes.

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9

Sander, Leonard M. "Kurt Jacobs: Stochastic Processes for Physicists." Journal of Statistical Physics 146, no. 4 (January 10, 2012): 880–81. http://dx.doi.org/10.1007/s10955-012-0419-8.

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10

Kvasnička, Vladimír. "Special kinetic models of selection processes in biomacromolecular systems." Collection of Czechoslovak Chemical Communications 53, no. 12 (1988): 3220–39. http://dx.doi.org/10.1135/cccc19883220.

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Physico-chemical models of selection processes on biomacromolecules - replicators are investigated. Three special cases are considered: 1) Replicators are selfreproduced with mutations, 2) selection process involving two or more substrates, and 3) selection process is controlled by external positive inflows of replicators. Simple tools of qualitative theory of differential equations are used, in particular the so-called linearization method based on the eigenvalues of Jacobi matrix evaluated at the given stationary state.

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11

Edward, Julian. "Jacobi Matrices and the Spectrum of the Neumann Operator on a Family of Riemann Surfaces." Canadian Journal of Mathematics 45, no. 4 (August 1, 1993): 709–26. http://dx.doi.org/10.4153/cjm-1993-040-0.

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AbstractThe Neumann operator is an operator on the boundary of a smooth manifold which maps the boundary value of a harmonic function to its normal derivative. The spectrum of the Neumann operator is studied on the curves bounding a family of Riemann surfaces. The Neumann operator is shown to be isospectral to a direct sum of symmetric Jacobi matrices, each acting on l2(ℤ). The Jacobi matrices are shown to be isospectral to generators of bilateral, linear birth-death processes. Using the connection between Jacobi matrices and continued fractions, it is shown that the eigenvalues of the Neumann operator must solve a certain equation involving hypergeometric functions. Study of the equation yields uniform bounds on the eigenvalues and also the asymptotics of the eigenvalues as the curves degenerate into a wedge of circles.

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12

Yadav, Sarjoo Prasad. "On the saturation order of approximation processes involving Jacobi polynomials." Journal of Approximation Theory 58, no. 1 (July 1989): 36–49. http://dx.doi.org/10.1016/0021-9045(89)90005-1.

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13

Assiotis, Theodoros. "Intertwinings for General $$\beta $$ β -Laguerre and $$\beta $$ β -Jacobi Processes." Journal of Theoretical Probability 32, no. 4 (July 11, 2018): 1880–91. http://dx.doi.org/10.1007/s10959-018-0842-0.

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14

Voit, Michael. "Some martingales associated with multivariate Jacobi processes and Aomoto’s Selberg integral." Indagationes Mathematicae 31, no. 3 (May 2020): 398–410. http://dx.doi.org/10.1016/j.indag.2020.02.005.

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15

Dung, Nguyen Tien, and Trinh Nhu Quynh. "Tail distribution of the integrated Jacobi diffusion process." Statistics, Optimization & Information Computing 8, no. 3 (July 1, 2020): 790–800. http://dx.doi.org/10.19139/soic-2310-5070-760.

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In this paper, we study the distribution of the integrated Jacobi diffusion processes with Brownian noise and fractional Brownian noise. Based on techniques of Malliavin calculus, we develop a unified method to obtain explicit estimates for the tail distribution of these integrated diffusions.

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16

Hermosilla, Cristopher, Richard Vinter, and Hasnaa Zidani. "Hamilton–Jacobi–Bellman equations for optimal control processes with convex state constraints." Systems & Control Letters 109 (November 2017): 30–36. http://dx.doi.org/10.1016/j.sysconle.2017.09.004.

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17

Voit, Michael. "Central limit theorems for hyperbolic spaces and Jacobi processes on $$[0,\infty [$$." Monatshefte für Mathematik 169, no. 3-4 (December 25, 2012): 441–68. http://dx.doi.org/10.1007/s00605-012-0460-3.

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18

Misawa, T. "A stochastic Hamilton-Jacobi theory in stochastic Hamiltonian mechanics for diffusion processes." Il Nuovo Cimento B Series 11 99, no. 2 (June 1987): 179–99. http://dx.doi.org/10.1007/bf02726581.

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19

Demni, Nizar, and Tarek Hamdi. "Inverse of the flow and moments of the free Jacobi process associated with one projection." Random Matrices: Theory and Applications 07, no. 02 (March 20, 2018): 1850001. http://dx.doi.org/10.1142/s2010326318500016.

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This paper is a companion to a series of papers devoted to the study of the spectral distribution of the free Jacobi process associated with a single projection. Actually, we note that the flow derived in [N. Demni and T. Hmidi, Spectral distribution of the free Jacobi process associated with one projection, Colloq. Math. 137(2) (2014) 271–296] solves a radial Löwner equation and as such, the general theory of Löwner equations implies that it is univalent in some connected region in the open unit disc. We also prove that its inverse defines the Aleksandrov–Clark measure at [Formula: see text] of some Herglotz function which is absolutely-continuous with an essentially bounded density. As a by-product, we deduce that [Formula: see text] does not belong to the continuous singular spectrum of the unitary operator whose spectral dynamics are governed by the flow. Moreover, we use a previous result due to the first author in order to derive an explicit, yet complicated, expression of the moments of both the unitary and the free Jacobi processes. The paper is closed with some remarks on the boundary behavior of the flow’s inverse.

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20

Chafik, Sanaa, Abdelhadi Larach, and Cherki Daoui. "Parallel Hierarchical Pre-Gauss-Seidel Value Iteration Algorithm." International Journal of Decision Support System Technology 10, no. 2 (April 2018): 1–22. http://dx.doi.org/10.4018/ijdsst.2018040101.

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The standard Value Iteration (VI) algorithm, referred to as Value Iteration Pre-Jacobi (PJ-VI) algorithm, is the simplest Value Iteration scheme, and the well-known algorithm for solving Markov Decision Processes (MDPs). In the literature, several versions of VI algorithm were developed in order to reduce the number of iterations: the VI Jacobi (VI-J) algorithm, the Value Iteration Pre-Gauss-Seidel (VI-PGS) algorithm and the VI Gauss-Seidel (VI-GS) algorithm. In this article, the authors combine the advantages of VI Pre Gauss-Seidel algorithm, the decomposition technique and the parallelism in order to propose a new Parallel Hierarchical VI Pre-Gauss-Seidel algorithm. Experimental results show that their approach performs better than the traditional VI schemes in the case where the global problem can be decomposed into smaller problems.

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21

MNIF, MOHAMED. "OPTIMAL RISK CONTROL UNDER MARKED POINT PROCESSES SHOCKS: A DYNAMIC PROGRAMMING DUALITY APPROACH." International Journal of Theoretical and Applied Finance 16, no. 07 (November 2013): 1350036. http://dx.doi.org/10.1142/s0219024913500362.

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We study the stochastic control problem of maximizing expected utility from terminal wealth under a nonbankruptcy constraint. The problem of the agent is to derive the optimal insurance strategy which reduces his exposure to the risk. This optimization problem is related to a suitable dual stochastic control problem in which the delicate boundary constraints disappear. We characterize the dual value function as the unique viscosity solution of the corresponding Hamilton Jacobi Bellman Variational Inequality (HJBVI in short). We characterize the optimal insurance strategy by the solution of the variational inequality which we solve numerically by using an algorithm based on policy iterations.

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22

Dzupire, Nelson Christopher, Philip Ngare, and Leo Odongo. "Pricing Basket Weather Derivatives on Rainfall and Temperature Processes." International Journal of Financial Studies 7, no. 3 (June 27, 2019): 35. http://dx.doi.org/10.3390/ijfs7030035.

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This paper follows an incomplete market pricing approach to analyze the evaluation of weather derivatives and the viability of a weather derivatives market in terms of hedging. A utility indifference method is developed for the specification of indifference prices for the seller and buyer of a basket of weather derivatives written on rainfall and temperature. The agent’s risk preference is described by an exponential utility function and the prices are derived by dynamic programming principles and corresponding Hamilton Jacobi-Bellman equations from the stochastic optimal control problems. It is found the indifference measure is equal to the physical measure as there is no correlation between the capital market and weather. The fair price of the derivative should be greater than the seller’s indifference price and less than the buyer’s indifference price for market viability and no arbitrage opportunities.

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23

Littlejohn, R. P. "An operation which inverts Bernoulli multiplication and associated stationary reversible Markov processes." Journal of Applied Probability 29, no. 1 (March 1992): 234–38. http://dx.doi.org/10.2307/3214810.

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A simple operation is described which inverts Bernoulli multiplication. It is used to define two classes of stationary reversible Markov processes with general marginal distribution. These are compared to the DAR(1) process of Jacobs and Lewis (1978). LJAR(1) is used to model ovulation rate time series.

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Littlejohn, R. P. "An operation which inverts Bernoulli multiplication and associated stationary reversible Markov processes." Journal of Applied Probability 29, no. 01 (March 1992): 234–38. http://dx.doi.org/10.1017/s0021900200106813.

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A simple operation is described which inverts Bernoulli multiplication. It is used to define two classes of stationary reversible Markov processes with general marginal distribution. These are compared to the DAR(1) process of Jacobs and Lewis (1978). LJAR(1) is used to model ovulation rate time series.

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25

Masjed-Jamei, Mohammad, and Gradimir Milovanovic. "Construction of Gaussian quadrature formulas for even weight functions." Applicable Analysis and Discrete Mathematics 11, no. 1 (2017): 177–98. http://dx.doi.org/10.2298/aadm1701177m.

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Instead of a quadrature rule of Gaussian type with respect to an even weight function on (?a, a) with n nodes, we construct the corresponding Gaussian formula on (0, a2) with only [(n+1)/2] nodes. Especially, such a procedure is important in the cases of nonclassical weight functions, when the elements of the corresponding three-diagonal Jacobi matrix must be constructed numerically. In this manner, the influence of numerical instabilities in the process of construction can be significantly reduced, because the dimension of the Jacobi matrix is halved. We apply this approach to Pollaczek?s type weight functions on (?1, 1), to the weight functions on R which appear in the Abel-Plana summation processes, as well as to a class of weight functions with four free parameters, which covers the generalized ultraspherical and Hermite weights. Some numerical examples are also included.

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26

Kühn, Franziska. "Viscosity solutions to Hamilton–Jacobi–Bellman equations associated with sublinear Lévy(-type) processes." Latin American Journal of Probability and Mathematical Statistics 16, no. 1 (2019): 531. http://dx.doi.org/10.30757/alea.v16-20.

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27

Costa, O. L. V., and F. Dufour. "Hamilton-Jacobi-Bellman inequality for the average control of piecewise deterministic Markov processes." Stochastics 91, no. 6 (November 13, 2018): 817–35. http://dx.doi.org/10.1080/17442508.2018.1546305.

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28

Chouchene, Frej, Léonard Gallardo, and Maher Mili. "The Heat Semigroup for the Jacobi–Dunkl Operator and the Related Markov Processes." Potential Analysis 25, no. 2 (July 15, 2006): 103–19. http://dx.doi.org/10.1007/s11118-006-9012-6.

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29

Gorin, V. E. "Noncolliding Jacobi processes as limits of Markov chains on the Gelfand–Tsetlin graph." Journal of Mathematical Sciences 158, no. 6 (April 16, 2009): 819–37. http://dx.doi.org/10.1007/s10958-009-9416-0.

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30

Murru, Nadir, and Lea Terracini. "Simultaneous approximations to p-adic numbers and algebraic dependence via multidimensional continued fractions." Ramanujan Journal 56, no. 1 (July 17, 2021): 67–86. http://dx.doi.org/10.1007/s11139-021-00466-z.

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AbstractUnlike the real case, there are not many studies and general techniques for providing simultaneous approximations in the field of p-adic numbers $$\mathbb Q_p$$ Q p . Here, we study the use of multidimensional continued fractions (MCFs) in this context. MCFs were introduced in $$\mathbb R$$ R by Jacobi and Perron as a generalization of continued fractions and they have been recently defined also in $$\mathbb Q_p$$ Q p . We focus on the dimension two and study the quality of the simultaneous approximation to two p-adic numbers provided by p-adic MCFs, where p is an odd prime. Moreover, given algebraically dependent p-adic numbers, we see when infinitely many simultaneous approximations satisfy the same algebraic relation. This also allows to give a condition that ensures the finiteness of the p-adic Jacobi–Perron algorithm when it processes some kinds of $$\mathbb Q$$ Q -linearly dependent inputs.

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31

Yilmaz, Adil, and Gazanfer Unal. "Chaoticity Properties of Fractionally Integrated Generalized Autoregressive Conditional Heteroskedastic Processes." Bulletin of Mathematical Sciences and Applications 15 (May 2016): 69–82. http://dx.doi.org/10.18052/www.scipress.com/bmsa.15.69.

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Fractionally integrated generalized autoregressive conditional heteroskedasticity (FIGARCH) arises in modeling of financial time series. FIGARCH is essentially governed by a system of nonlinear stochastic difference equations.In this work, we have studied the chaoticity properties of FIGARCH (p,d,q) processes by computing mutual information, correlation dimensions, FNNs (False Nearest Neighbour), the largest Lyapunov exponents (LLE) for both the stochastic difference equation and for the financial time series by applying Wolf’s algorithm, Kant’z algorithm and Jacobian algorithm. Although Wolf’s algorithm produced positive LLE’s, Kantz’s algorithm and Jacobian algorithm which are subsequently developed methods due to insufficiency of Wolf’s algorithm generated negative LLE’s constantly.So, as well as experimenting Wolf’s methods’ inefficiency formerly pointed out by Rosenstein (1993) and later Dechert and Gencay (2000), based on Kantz’s and Jacobian algorithm’s negative LLE outcomes, we concluded that it can be suggested that FIGARCH (p,d,q) is not deterministic chaotic process.

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32

ADLER, MARK, PIERRE VAN MOERBEKE, and DONG WANG. "RANDOM MATRIX MINOR PROCESSES RELATED TO PERCOLATION THEORY." Random Matrices: Theory and Applications 02, no. 04 (October 2013): 1350008. http://dx.doi.org/10.1142/s2010326313500081.

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This paper studies a number of matrix models of size n and the associated Markov chains for the eigenvalues of the models for consecutive n's. They are consecutive principal minors for two of the models, GUE with external source and the multiple Laguerre matrix model, and merely properly defined consecutive matrices for the third one, the Jacobi–Piñeiro model; nevertheless the eigenvalues of the consecutive models all interlace. We show: (i) For each of those finite models, we give the transition probability of the associated Markov chain and the joint distribution of the entire interlacing set of eigenvalues; we show this is a determinantal point process whose extended kernels share many common features. (ii) To each of these models and their set of eigenvalues, we associate a last-passage percolation model, either finite percolation or percolation along an infinite strip of finite width, yielding a precise relationship between the last-passage times and the eigenvalues. (iii) Finally, it is shown that for appropriate choices of exponential distribution on the percolation, with very small means, the rescaled last-passage times lead to the Pearcey process; this should connect the Pearcey statistics with random directed polymers.

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Gonzalez Granada, Jose Rodrigo, Luis Fernado Plaza Galvez, and Olena Vasyunkina. "From Black-Scholes to Hamilton-Jacobi." Contemporary Engineering Sciences 11, no. 90 (2018): 4455–63. http://dx.doi.org/10.12988/ces.2018.89495.

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Fujita, Toshiharu, and Akifumi Kira. "Mutually Dependent Markov Decision Processes." Journal of Advanced Computational Intelligence and Intelligent Informatics 18, no. 6 (November 20, 2014): 992–98. http://dx.doi.org/10.20965/jaciii.2014.p0992.

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In this paper, we introduce a basic framework for mutually dependent Markov decision processes (MDMDP) showing recursive mutual dependence. Our model is structured upon two types of finite-stage Markov decision processes. At each stage, the reward in one process is given by the optimal value of the alternative process problem, whose initial state is determined by the current state and decision in the original process. We formulate the MDMDP model and derive mutually dependent recursive equations by dynamic programming. Furthermore, MDMDP is illustrated in a numerical example. The model enables easier treatment of some classes of complex multi-stage decision processes.

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Flajolet, Philippe, and Fabrice Guillemin. "The formal theory of birth-and-death processes, lattice path combinatorics and continued fractions." Advances in Applied Probability 32, no. 03 (September 2000): 750–78. http://dx.doi.org/10.1017/s0001867800010247.

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Classic works of Karlin and McGregor and Jones and Magnus have established a general correspondence between continuous-time birth-and-death processes and continued fractions of the Stieltjes-Jacobi type together with their associated orthogonal polynomials. This fundamental correspondence is revisited here in the light of the basic relation between weighted lattice paths and continued fractions otherwise known from combinatorial theory. Given that sample paths of the embedded Markov chain of a birth-and-death process are lattice paths, Laplace transforms of a number of transient characteristics can be obtained systematically in terms of a fundamental continued fraction and its family of convergent polynomials. Applications include the analysis of evolutions in a strip, upcrossing and downcrossing times under flooring and ceiling conditions, as well as time, area, or number of transitions while a geometric condition is satisfied.

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36

Bandini, Elena. "Optimal control of piecewise deterministic Markov processes: a BSDE representation of the value function." ESAIM: Control, Optimisation and Calculus of Variations 24, no. 1 (January 2018): 311–54. http://dx.doi.org/10.1051/cocv/2017006.

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We consider an infinite-horizon discounted optimal control problem for piecewise deterministic Markov processes, where a piecewise open-loop control acts continuously on the jump dynamics and on the deterministic flow. For this class of control problems, the value function can in general be characterized as the unique viscosity solution to the corresponding Hamilton−Jacobi−Bellman equation. We prove that the value function can be represented by means of a backward stochastic differential equation (BSDE) on infinite horizon, driven by a random measure and with a sign constraint on its martingale part, for which we give existence and uniqueness results. This probabilistic representation is known as nonlinear Feynman−Kac formula. Finally we show that the constrained BSDE is related to an auxiliary dominated control problem, whose value function coincides with the value function of the original non-dominated control problem.

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37

Flajolet, Philippe, and Fabrice Guillemin. "The formal theory of birth-and-death processes, lattice path combinatorics and continued fractions." Advances in Applied Probability 32, no. 3 (September 2000): 750–78. http://dx.doi.org/10.1239/aap/1013540243.

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Classic works of Karlin and McGregor and Jones and Magnus have established a general correspondence between continuous-time birth-and-death processes and continued fractions of the Stieltjes-Jacobi type together with their associated orthogonal polynomials. This fundamental correspondence is revisited here in the light of the basic relation between weighted lattice paths and continued fractions otherwise known from combinatorial theory. Given that sample paths of the embedded Markov chain of a birth-and-death process are lattice paths, Laplace transforms of a number of transient characteristics can be obtained systematically in terms of a fundamental continued fraction and its family of convergent polynomials. Applications include the analysis of evolutions in a strip, upcrossing and downcrossing times under flooring and ceiling conditions, as well as time, area, or number of transitions while a geometric condition is satisfied.

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38

Swishchuk, Anatoliy, and Nikolaos Limnios. "Controlled Discrete-Time Semi-Markov Random Evolutions and Their Applications." Mathematics 9, no. 2 (January 13, 2021): 158. http://dx.doi.org/10.3390/math9020158.

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In this paper, we introduced controlled discrete-time semi-Markov random evolutions. These processes are random evolutions of discrete-time semi-Markov processes where we consider a control. applied to the values of random evolution. The main results concern time-rescaled weak convergence limit theorems in a Banach space of the above stochastic systems as averaging and diffusion approximation. The applications are given to the controlled additive functionals, controlled geometric Markov renewal processes, and controlled dynamical systems. We provide dynamical principles for discrete-time dynamical systems such as controlled additive functionals and controlled geometric Markov renewal processes. We also produce dynamic programming equations (Hamilton–Jacobi–Bellman equations) for the limiting processes in diffusion approximation such as controlled additive functionals, controlled geometric Markov renewal processes and controlled dynamical systems. As an example, we consider the solution of portfolio optimization problem by Merton for the limiting controlled geometric Markov renewal processes in diffusion approximation scheme. The rates of convergence in the limit theorems are also presented.

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39

Chripkó, Ágnes. "Weighted approximation via Θ-summations of Fourier-Jacobi series." Studia Scientiarum Mathematicarum Hungarica 47, no. 2 (June 1, 2010): 139–54. http://dx.doi.org/10.1556/sscmath.2009.1121.

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This paper is devoted to the study of Θ-summability of Fourier-Jacobi series. We shall construct such processes (using summations) that are uniformly convergent in a Banach space (\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$C_{w_{\gamma ,\delta } } ,\parallel \cdot \parallel _{w_{\gamma ,\delta } }$$ \end{document}) of continuous functions. Some special cases are also considered, such as the Fejér, de la Vallée Poussin, Cesàro, Riesz and Rogosinski summations. Our aim is to give such conditions with respect to Jacobi weights wγ,δ , wα,β and to summation matrix Θ for which the uniform convergence holds for all f ∈ \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$C_{w_{\gamma ,\delta } }$$ \end{document}. Order of convergence will also be investigated. The results and the methods are analogues to the discrete case (see [16] and [17]).

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40

Byrne, Patrick. "ECOLOGY, ECONOMY AND REDEMPTION AS DYNAMIC: THE CONTRIBUTIONS OF JANE JACOBS AND BERNARD LONERGAN." Worldviews: Global Religions, Culture, and Ecology 7, no. 1-2 (2003): 5–26. http://dx.doi.org/10.1163/156853503321916192.

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AbstractBernard Lonergan, S.J. and Jane Jacobs have devoted much of their intellectual careers to thinking out the dynamic natural-human environment. Lonergan and Jacobs worked in very different lines of research - systematic theology and urban economics, respectively. Despite predictable differences in their thought, there are also remarkable commonalities in their analyses. Both thinkers have argued that the same dynamic principles that govern the functioning of natural ecologies are also to be found when human social and economic systems function well, but are absent when human systems go wrong. Both have argued that the violation of principles that pertain to natural ecologies is destructive not only of the natural environment, but of communal and economic well-being as well. Jacobs came to prominence with the 1961 publication of her classic, The Death and Life of Great American Cities. She has since gone on to extend her analysis to the unique characteristics of urban economics in several books and articles. In her most recent book The Nature of Economies (2000), Jacobs draws the results of her previous work on urban economic patterns into a synthesis with recent insights into biological systems. She argues that exactly the same principles (or "processes" as she prefers to call them) that sustain vital, evolving natural ecologies also underpin robust and dynamic economies. Where Jacobs's work gives a richly detailed account of the processes shared alike by natural and human systems, Lonergan developed a parallel, integral account of natural processes, human social and economic organization, and the "economy of salvation." In his classic work, Insight, Lonergan argues that the dynamics of human innovations and self-correction correspond in striking ways to the emergence, growth, development, and decline in the natural order. Unlike natural ecologies, however, the possibilities of genuine social and economic development are distorted, Lonergan argues, by the forces of "bias." In his role of theologian, Lonergan goes on to explore how divine grace heals the distorted dynamics of natural and human ecologies.

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Sym, Antoni. "Vortex filament motion in terms of Jacobi theta functions." Fluid Dynamics Research 3, no. 1-4 (September 1988): 151–56. http://dx.doi.org/10.1016/0169-5983(88)90059-7.

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Jing, Shi, and Yan Xin-li. "Analytical Solutions for the Elastic Circular Rod Nonlinear Wave, Boussinesq, and Dispersive Long Wave Equations." Journal of Applied Mathematics 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/487571.

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The solving processes of the homogeneous balance method, Jacobi elliptic function expansion method, fixed point method, and modified mapping method are introduced in this paper. By using four different methods, the exact solutions of nonlinear wave equation of a finite deformation elastic circular rod, Boussinesq equations and dispersive long wave equations are studied. In the discussion, the more physical specifications of these nonlinear equations, have been identified and the results indicated that these methods (especially the fixed point method) can be used to solve other similar nonlinear wave equations.

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43

Christensen, Sören, Albrecht Irle, and Andreas Ludwig. "Optimal portfolio selection under vanishing fixed transaction costs." Advances in Applied Probability 49, no. 4 (November 17, 2017): 1116–43. http://dx.doi.org/10.1017/apr.2017.36.

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Abstract In this paper asymptotic results in a long-term growth rate portfolio optimization model under both fixed and proportional transaction costs are obtained. More precisely, the convergence of the model when the fixed costs tend to 0 is investigated. A suitable limit model with purely proportional costs is introduced and the convergence of optimal boundaries, asymptotic growth rates, and optimal risky fraction processes is rigorously proved. The results are based on an in-depth analysis of the convergence of the solutions to the corresponding Hamilton–Jacobi–Bellman equations.

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Kyprianou, Andreas E., Ronnie Loeffen, and José-Luis Pérez. "Optimal Control with Absolutely Continuous Strategies for Spectrally Negative Lévy Processes." Journal of Applied Probability 49, no. 01 (March 2012): 150–66. http://dx.doi.org/10.1017/s0021900200008913.

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In the last few years there has been renewed interest in the classical control problem of de Finetti (1957) for the case where the underlying source of randomness is a spectrally negative Lévy process. In particular, a significant step forward was made by Loeffen (2008), who showed that a natural and very general condition on the underlying Lévy process which allows one to proceed with the analysis of the associated Hamilton-Jacobi-Bellman equation is that its Lévy measure is absolutely continuous, having completely monotone density. In this paper we consider de Finetti's control problem, but with the restriction that control strategies are absolutely continuous with respect to the Lebesgue measure. This problem has been considered by Asmussen and Taksar (1997), Jeanblanc-Picqué and Shiryaev (1995), and Boguslavskaya (2006) in the diffusive case, and Gerber and Shiu (2006) for the case of a Cramér-Lundberg process with exponentially distributed jumps. We show the robustness of the condition that the underlying Lévy measure has a completely monotone density and establish an explicit optimal strategy for this case that envelopes the aforementioned existing results. The explicit optimal strategy in question is the so-called refraction strategy.

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Kyprianou, Andreas E., Ronnie Loeffen, and José-Luis Pérez. "Optimal Control with Absolutely Continuous Strategies for Spectrally Negative Lévy Processes." Journal of Applied Probability 49, no. 1 (March 2012): 150–66. http://dx.doi.org/10.1239/jap/1331216839.

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In the last few years there has been renewed interest in the classical control problem of de Finetti (1957) for the case where the underlying source of randomness is a spectrally negative Lévy process. In particular, a significant step forward was made by Loeffen (2008), who showed that a natural and very general condition on the underlying Lévy process which allows one to proceed with the analysis of the associated Hamilton-Jacobi-Bellman equation is that its Lévy measure is absolutely continuous, having completely monotone density. In this paper we consider de Finetti's control problem, but with the restriction that control strategies are absolutely continuous with respect to the Lebesgue measure. This problem has been considered by Asmussen and Taksar (1997), Jeanblanc-Picqué and Shiryaev (1995), and Boguslavskaya (2006) in the diffusive case, and Gerber and Shiu (2006) for the case of a Cramér-Lundberg process with exponentially distributed jumps. We show the robustness of the condition that the underlying Lévy measure has a completely monotone density and establish an explicit optimal strategy for this case that envelopes the aforementioned existing results. The explicit optimal strategy in question is the so-called refraction strategy.

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46

Tinoco, Alexandre. "Das economias de aglomeração às externalidades dinâmicas de conhecimento: por uma releitura de São Paulo." Revista Brasileira de Estudos Urbanos e Regionais 5, no. 1 (May 31, 2003): 47. http://dx.doi.org/10.22296/2317-1529.2003v5n1p47.

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Ao reconstituir o debate sobre especialização/diversificação setorial como motor do desenvolvimento urbano, este artigo retraça a construção dos conceitos de externalidades dinâmicas MAR e Jacobs e os reutiliza para o estudo dos processos inovativos das empresas industriais da Região Metropolitana de São Paulo. Com isso, busca aprofundar o debate teórico e a interpretação da realidade econômica paulistana da década de 1990, de um enfoque baseado nas estratégias dos agentes econômicos aí presentes. Para tanto, é necessário compreender as estratégias de inserção a redes de informação para o processo inovativo, com base na construção de um portfolio setorial de fontes.Palavras-chave: economias de aglomeração; externalidades de conhecimento; inovação; especialização; diversificação. From the accumulation economy to the dynamic externalities of knowledge: for a new reading of São PauloAbstract: Reconstructing the debate on the specialization/diversification of the economic activity as the engine of the urban development, this article retraces the construction of the concepts of dynamic externalities MAR and Jacobs and reuses them for the study of the innovative processes of the industrial firms of the Metropolitan Region of São Paulo. Therefore, it searches to deepen the following debates: one in the field of the theoretical construction and other in the field of interpretation of economic reality of São Paulo in the decade of 1990. The empirical instruments for such are based on the construction of an industry portfolio of sources for the innovative process.Keywords: economies of agglomeration; externalities of knowledge; innovation; specialization; diversification.

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Yan, Wei. "Closed-Form Optimal Strategies of Continuous-Time Options with Stochastic Differential Equations." Complexity 2017 (2017): 1–11. http://dx.doi.org/10.1155/2017/8734235.

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A continuous-time portfolio selection with options based on risk aversion utility function in financial market is studied. The different price between sale and purchase of options is introduced in this paper. The optimal investment-consumption problem is formulated as a continuous-time mathematical model with stochastic differential equations. The prices processes follow jump-diffusion processes (Weiner process and Poisson process). Then the corresponding Hamilton-Jacobi-Bellman (HJB) equation of the problem is represented and its solution is obtained in different conditions. The above results are applied to a special case under a Hyperbolic Absolute Risk Aversion (HARA) utility function. The optimal investment-consumption strategies about HARA utility function are also derived. Finally, an example and some discussions illustrating these results are also presented.

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Cortés, Emilio. "On extremal paths for stochastic processes that involve step potentials and the generalized Hamilton-Jacobi equation." Physica A: Statistical Mechanics and its Applications 182, no. 1-2 (March 1992): 228–39. http://dx.doi.org/10.1016/0378-4371(92)90240-q.

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Hak, Jacob Bart. "Alicia Caporaso (ed.) Formation Processes of Maritime Archaeological Landscapes (Jacob Bart Hak)." Northern Mariner / Le marin du nord 30, no. 1 (June 10, 2021): 74. http://dx.doi.org/10.25071/2561-5467.94.

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Ватутин, Владимир Алексеевич, and Vladimir Alekseevich Vatutin. "Рецензия на книги Jacobs К. “Discrete Stochastics”, Resnick S. “Adventures in Stochastic Processes”." Teoriya Veroyatnostei i ee Primeneniya 41, no. 3 (1996): 711–14. http://dx.doi.org/10.4213/tvp3189.

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Journal articles on the topic 'Processus de Jacobi'

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