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Relevant bibliographies by topics / Brownian motion

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Academic literature on the topic 'Brownian motion'

Author: Grafiati

Published: 4 June 2021

Last updated: 11 June 2025

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Journal articles on the topic "Brownian motion"

1

Burdzy, Krzysztof, and David Nualart. "Brownian motion reflected on Brownian motion." Probability Theory and Related Fields 122, no. 4 (2002): 471–93. http://dx.doi.org/10.1007/s004400100165.

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Chernov, N., and D. Dolgopyat. "Brownian Brownian motion. I." Memoirs of the American Mathematical Society 198, no. 927 (2009): 0. http://dx.doi.org/10.1090/memo/0927.

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Blanco Castañeda, Liliana. "UNA CONSTRUCCION DEL "BRANCHING-BROWNIAN-MOTION"." Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales 22, no. 83 (2024): 213–20. http://dx.doi.org/10.18257/raccefyn.22(83).1998.2902.

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Xiong, Jie, and Xiaowen Zhou. "On the Duality between Coalescing Brownian Motions." Canadian Journal of Mathematics 57, no. 1 (2005): 204–24. http://dx.doi.org/10.4153/cjm-2005-009-2.

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AbstractA duality formula is found for coalescing Brownian motions on the real line. It is shown that the joint distribution of a coalescing Brownian motion can be determined by another coalescing Brownian motion running backward. This duality is used to study a measure-valued process arising as the high density limit of the empirical measures of coalescing Brownian motions.

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Rao, B. V. "Brownian Motion." Resonance 26, no. 1 (2021): 89–104. http://dx.doi.org/10.1007/s12045-020-1107-7.

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Deutsch, Daniel H. "Brownian motion." Nature 357, no. 6377 (1992): 354. http://dx.doi.org/10.1038/357354c0.

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Parisi, Giorgio. "Brownian motion." Nature 433, no. 7023 (2005): 221. http://dx.doi.org/10.1038/433221a.

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Lavenda, Bernard H. "Brownian Motion." Scientific American 252, no. 2 (1985): 70–85. http://dx.doi.org/10.1038/scientificamerican0285-70.

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Balla, Chandra Shekar, C. Haritha, Kishan Naikoti, and A. M. Rashad. "Bioconvection in nanofluid-saturated porous square cavity containing oxytactic microorganisms." International Journal of Numerical Methods for Heat & Fluid Flow 29, no. 4 (2019): 1448–65. http://dx.doi.org/10.1108/hff-05-2018-0238.

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PurposeThe purpose of this paper is to investigate the bioconvection flow in a porous square cavity saturated with both oxytactic microorganism and nanofluids.Design/methodology/approachThe impacts of the effective parameters such as Rayleigh number, bioconvection number, Peclet number and thermophoretic force, Brownan motion and Lewis number reduces the flow strength in the cavity on the flow strength, oxygen density distribution, motile isoconcentrations and heat transfer performance are investigated using a finite volume approach.FindingsThe results obtained showed that the average Nusselt number is increased with Peclet number, Lewis number, Brownian motion and thermophoretic force. Also, the average Sherwood number increased with Brownian motion and Peclet number and decreased with thermophoretic force. It is concluded that the flow strength is pronounced with Rayleigh number, bioconvection number, Peclet number and thermophoretic force. Brownan motion and Lewis number reduce the flow strength in the cavity.Originality/valueThere is no published study in the literature about sensitivity analysis of Brownian motion and thermophoresis force effects on the bioconvection heat transfer in a square cavity filled by both nanofluid and oxytactic microorganisms.

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Engelbert, Hans-Jürgen, and Jochen Wolf. "Dirichlet functions of reflected Brownian motion." Mathematica Bohemica 125, no. 2 (2000): 235–47. http://dx.doi.org/10.21136/mb.2000.125954.

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Dissertations / Theses on the topic "Brownian motion"

1

Rings, Daniel. "Hot Brownian Motion." Doctoral thesis, Universitätsbibliothek Leipzig, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-102186.

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The theory of Brownian motion is a cornerstone of modern physics. In this thesis, we introduce a nonequilibrium extension to this theory, namely an effective Markovian theory of the Brownian motion of a heated nanoparticle. This phenomenon belongs to the class of nonequilibrium steady states (NESS) and is characterized by spatially inhomogeneous temperature and viscosity fields extending in the solvent surrounding the nanoparticle. The first chapter provides a pedagogic introduction to the subject and a concise summary of our main results and summarizes their implications for future developments and innovative applications. The derivation of our main results is based on the theory of fluctuating hydrodynamics, which we introduce and extend to NESS conditions, in the second chapter. We derive the effective temperature and the effective friction coefficient for the generalized Langevin equation describing the Brownian motion of a heated nanoparticle. As major results, we find that these parameters obey a generalized Stokes–Einstein relation, and that, to first order in the temperature increment of the particle, the effective temperature is given in terms of a set of universal numbers. In chapters three and four, these basic results are made explicit for various realizations of hot Brownian motion. We show in detail, that different degrees of freedom are governed by distinct effective parameters, and we calculate these for the rotational and translational motion of heated nanobeads and nanorods. Whenever possible, analytic results are provided, and numerically accurate approximation methods are devised otherwise. To test and validate all our theoretical predictions, we present large-scale molecular dynamics simulations of a Lennard-Jones system, in chapter five. These implement a state-of-the-art GPU-powered parallel algorithm, contributed by D. Chakraborty. Further support for our theory comes from recent experimental observations of gold nanobeads and nanorods made in the the groups of F. Cichos and M. Orrit. We introduce the theoretical concept of PhoCS, an innovative technique which puts the selective heating of nanoscopic tracer particles to good use. We conclude in chapter six with some preliminary results about the self-phoretic motion of so-called Janus particles. These two-faced hybrids with a hotter and a cooler side perform a persistent random walk with the persistence only limited by their hot rotational Brownian motion. Such particles could act as versatile laser-controlled nanotransporters or nanomachines, to mention just the most obvious future nanotechnological applications of hot Brownian motion.

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Rings, Daniel, Romy Radünz, Frank Cichos, and Klaus Kroy. "Hot brownian motion." Universitätsbibliothek Leipzig, 2015. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-190908.

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Rings, Daniel, Romy Radünz, Frank Cichos, and Klaus Kroy. "Hot brownian motion." Diffusion fundamentals 11 (2009) 75, S. 1-2, 2009. https://ul.qucosa.de/id/qucosa%3A14040.

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Trefán, György. "Deterministic Brownian Motion." Thesis, University of North Texas, 1993. https://digital.library.unt.edu/ark:/67531/metadc279262/.

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The goal of this thesis is to contribute to the ambitious program of the foundation of developing statistical physics using chaos. We build a deterministic model of Brownian motion and provide a microscpoic derivation of the Fokker-Planck equation. Since the Brownian motion of a particle is the result of the competing processes of diffusion and dissipation, we create a model where both diffusion and dissipation originate from the same deterministic mechanism - the deterministic interaction of that particle with its environment. We show that standard diffusion which is the basis of the Fokker-Planck equation rests on the Central Limit Theorem, and, consequently, on the possibility of deriving it from a deterministic process with a quickly decaying correlation function. The sensitive dependence on initial conditions, one of the defining properties of chaos insures this rapid decay. We carefully address the problem of deriving dissipation from the interaction of a particle with a fully deterministic nonlinear bath, that we term the booster. We show that the solution of this problem essentially rests on the linear response of a booster to an external perturbation. This raises a long-standing problem concerned with Kubo's Linear Response Theory and the strong criticism against it by van Kampen. Kubo's theory is based on a perturbation treatment of the Liouville equation, which, in turn, is expected to be totally equivalent to a first-order perturbation treatment of single trajectories. Since the boosters are chaotic, and chaos is essential to generate diffusion, the single trajectories are highly unstable and do not respond linearly to weak external perturbation. We adopt chaotic maps as boosters of a Brownian particle, and therefore address the problem of the response of a chaotic booster to an external perturbation. We notice that a fully chaotic map is characterized by an invariant measure which is a continuous function of the control parameters of the map. Consequently if the external perturbation is made to act on a control parameter of the map, we show that the booster distribution undergoes slight modifications as an effect of the weak external perturbation, thereby leading to a linear response of the mean value of the perturbed variable of the booster. This approach to linear response completely bypasses the criticism of van Kampen. The joint use of these two phenomena, diffusion and friction stemming from the interaction of the Brownian particle with the same booster, makes the microscopic derivation of a Fokker-Planck equation and Brownian motion, possible.

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Hobson, Tim. "Slowly-coalescing Brownian motion." Thesis, University of Warwick, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.487910.

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An interacting particle system is constructed in which a collection of independent Brownian motions are subject to the rule that each pair of particles shall coalesce at a rate given formally by ). dLt , where {Lt : t ~ O} is the intersection local time of the pair. This interaction mechanism is referred to as slowly-coalescing, in contrast to the more standard model in which particles coalesce immediately on collision. The process is shown to be the weak limit of a sequence of coalescing symmeteric random walks on the lattice n-1Z. Our indirect argument exploits the existence of a dual Markov process at both the discrete and the continuous level. By endowing each of the slowly-coalescing Brownian particles with a weight we are able to establish a more intimate duality, the dual process being the solution of a stochastic heat equation driven by Fisher-Wright noise.

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Mather, William Hardeman. "Rectified Brownian Motion in Biology." Diss., Georgia Institute of Technology, 2007. http://hdl.handle.net/1853/16244.

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Nanoscale biological systems operate in the presence of overwhelming viscous drag and thermal diffusion, thus invalidating the use of macroscopically oriented thinking to explain such systems. Rectified Brownian motion (RBM), in contrast, is a distinctly nanoscale approach that thrives in thermal environments. The thesis discusses both the foundations and applications of RBM, with an emphasis on nano-biology. Results from stochastic non-equilibrium steady state theory are used to motivate a compelling definition for RBM. It follows that RBM is distinct from both the so-called power stroke and Brownian ratchet approaches to nanoscale mechanisms. Several physical examples provide a concrete foundation for these theoretical arguments. Notably, the molecular motors kinesin and myosin V are proposed to function by means of a novel RBM mechanism: strain-induced bias amplification. The conclusion is reached that RBM is a versatile and robust approach to nanoscale biology.

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Neves, Susana de Matos. "Fractional Brownian Motion in Finance." Master's thesis, Instituto Superior de Economia e Gestão, 2012. http://hdl.handle.net/10400.5/10326.

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Mestrado em Matemática Financeira<br>Algumas das propriedades estatísticas dos dados financeiros são comuns a uma ampla variedade de mercados: a propriedade de memória longa, as caudas pesadas, assimetria (ganho / perda de assimetria), saltos, agrupamento de volatilidade, etc. A necessidade de procurar novos modelos de produtos financeiros tem aumentado nas últimas décadas devido à incapacidade dos actuais modelos explicarem algumas dessas propriedades estatísticas. Este trabalho tem como objetivo dar uma visão geral de alguns estudos que foram feitos relativamente à aplicação às finanças do movimento Browniano fracionário, em particular o trabalho de Paolo Guasoni e Cheridito Patrick, que mostram que, se assumirmos certas restrições, podemos eliminar oportunidades de arbitragem. Além disso, também são apresentados estudos empíricos com dados de mercado, com o objectivo de mostrar como se pode obter um estimador para o índice Hurst (o parâmetro do movimento Browniano fracionário). Para este fim, foram utilizados dois métodos, o método Rescaled Range e o método modificado do Rescaled Range. Este estudo permite-nos discutir o efeito de memória nas séries temporais de alguns índices de mercado.<br>Some of the statistical properties of the financial data are common to a wide variety of markets: long-range dependence properties, heavy tails, skewness (gain/loss asymmetry), jumps, volatility clustering, etc. The need to seek new models for financial products has increased in recent decades due to the inability of current models to explain some of these facts. One of these models is fractional Brownian motion. This work aims to give an overview of some studies that were done on the financial applications of fractional Brownian motion, in particular the work of Paolo Guasoni and Patrick Cheridito which shows that if we assume certain restrictions, we can eliminate arbitrage opportunities. Moreover, we also present empirical studies with market data, in order to show how to obtain an estimator for the Hurst index (the fractional Brownian motion parameter). To this end, we used two methods, the Rescaled Range Analysis and the modified Rescaled Range Analysis. This study allows us to discuss the effect of memory on the time series of some market indices.

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Inkaya, Alper. "Option Pricing With Fractional Brownian Motion." Master's thesis, METU, 2011. http://etd.lib.metu.edu.tr/upload/12613736/index.pdf.

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Traditional financial modeling is based on semimartingale processes with stationary and independent increments. However, empirical investigations on financial data does not always support these assumptions. This contradiction showed that there is a need for new stochastic models. Fractional Brownian motion (fBm) was proposed as one of these models by Benoit Mandelbrot. FBm is the only continuous Gaussian process with dependent increments. Correlation between increments of a fBm changes according to its self-similarity parameter H. This property of fBm helps to capture the correlation dynamics of the data and consequently obtain better forecast results. But for values of H different than 1/2, fBm is not a semimartingale and classical Ito formula does not exist in that case. This gives rise to need for using the white noise theory to construct integrals with respect to fBm and obtain fractional Ito formulas. In this thesis, the representation of fBm and its fundamental properties are examined. Construction of Wick-Ito-Skorohod (WIS) and fractional WIS integrals are investigated. An Ito type formula and Girsanov type theorems are stated. The financial applications of fBm are mentioned and the Black&amp<br>Scholes price of a European call option on an asset which is assumed to follow a geometric fBm is derived. The statistical aspects of fBm are investigated. Estimators for the self-similarity parameter H and simulation methods of fBm are summarized. Using the R/S methodology of Hurst, the estimations of the parameter H are obtained and these values are used to evaluate the fractional Black&amp<br>Scholes prices of a European call option with different maturities. Afterwards, these values are compared to Black&amp<br>Scholes price of the same option to demonstrate the effect of long-range dependence on the option prices. Also, estimations of H at different time scales are obtained to investigate the multiscaling in financial data. An outlook of the future work is given.

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Lange, Rutger-Jan. "Brownian motion and multidimensional decision making." Thesis, University of Cambridge, 2012. https://www.repository.cam.ac.uk/handle/1810/243402.

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This thesis consists of three self-contained parts, each with its own abstract, body, references and page numbering. Part I, 'Potential theory, path integrals and the Laplacian of the indicator', finds the transition density of absorbed or reflected Brownian motion in a d-dimensional domain as a Feynman-Kac functional involving the Laplacian of the indicator, thereby relating the hitherto unrelated fields of classical potential theory and path integrals. Part II, 'The problem of alternatives', considers parallel investment in alternative technologies or drugs developed over time, where there can be only one winner. Parallel investment accelerates the search for the winner, and increases the winner's expected performance, but is also costly. To determine which candidates show sufficient performance and/or promise, we find an integral equation for the boundary of the optimal continuation region. Part III, 'Optimal support for renewable deployment', considers the role of government subsidies for renewable technologies. Rapidly diminishing subsidies are cheaper for taxpayers, but could prematurely kill otherwise successful technologies. By contrast, high subsidies are not only expensive but can also prop up uneconomical technologies. To analyse this trade-off we present a new model for technology learning that makes capacity expansion endogenous. There are two reasons for this standalone structure. First, the target readership is divergent. Part I concerns mathematical physics, Part II operations research, and Part III policy. Readers interested in specific parts can thus read these in isolation. Those interested in the thesis as a whole may prefer to read the three introductions first. Second, the separate parts are only partially interconnected. Each uses some theory from the preceding part, but not all of it; e.g. Part II uses only a subset of the theory from Part I. The quickest route to Part III is therefore not through the entirety of the preceding parts. Furthermore, those instances where results from previous parts are used are clearly indicated.

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Howitt, Christopher John. "Stochastic flows and sticky Brownian motion." Thesis, University of Warwick, 2007. http://wrap.warwick.ac.uk/56226/.

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Sticky Brownian motion is a one-dimensional diffusion with the property that the amount of time the process spends at zero is of positive Lebesgue measure and yet the process does not stay at zero for any positive interval of time. Sticky Brownian motion can be considered as qualitatively between standard Brownian motion and Brownian motion absorbed at zero. A system of coalescing Brownian motions is a collection of paths, where each path behaves as a Brownian motion independent of all other paths until the first time two paths meet, at which point the two paths that have just met behave is a single Brownian motion independent of all remaining paths. Thus the difference between any two paths of a system of coalescing Brownian motion behaves as a Brownian motion absorbed at zero. In this thesis we consider systems of Brownian paths, where the difference between any two paths behaves as a sticky Brownian motion rather than a coalescing Brownian motion. We consider systems of sticky Brownian motions starting from points in continuous time and space. The evolution of systems of this type may be described by means of a stochastic flow of kernels. A stochastic flow of kernels is characterised by its N-point motions which form a consistent family of Brownian motions. We characterise such a consistent family such that the difference between any pair of coordinates behaves as a sticky Brownian motion. The Brownian web is a way of describing a system of coalescing Brownian motions starting in any point in space and time. We describe a coupling of Brownian webs such that the difference between one path in each web behaves as a sticky Brownian motion. Then by conditioning one Brownian web on the other we can construct a stochastic flow of kernels. Finally we discuss the concept of duality in relation to flows and we prove some minor results relating to these dualities.

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Books on the topic "Brownian motion"

1

1972-, Dolgopyat Dmitry, ed. Brownian Brownian motion-I. American Mathematical Society, 2009.

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Philipse, Albert P. Brownian Motion. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-98053-9.

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Pomerance, Murray. Brownian motion. Trois O, 1994.

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(Yuval), Peres Y., Schramm Oded, and Werner Wendelin 1968-, eds. Brownian motion. Cambridge University Press, 2010.

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Löffler, Andreas, and Lutz Kruschwitz. The Brownian Motion. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-20103-6.

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Wiersema, Ubbo F. Brownian motion calculus. John Wiley & Sons, 2008.

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Wiersema, Ubbo F. Brownian Motion Calculus. John Wiley & Sons, Ltd., 2008.

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Mansuy, Roger, and Marc Yor. Aspects of Brownian Motion. Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-49966-4.

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Lampo, Aniello, Miguel Ángel García March, and Maciej Lewenstein. Quantum Brownian Motion Revisited. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-16804-9.

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Earnshaw, Robert C., and Elizabeth M. Riley. Brownian motion: Theory, modelling and applications. Nova Science Publishers, 2011.

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Book chapters on the topic "Brownian motion"

1

Philipse, Albert P. "Brownian Displacements." In Brownian Motion. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-98053-9_6.

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Borodin, Andrei N., and Paavo Salminen. "Brownian Motion." In Handbook of Brownian Motion — Facts and Formulae. Birkhäuser Basel, 1996. http://dx.doi.org/10.1007/978-3-0348-7652-0_4.

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Borodin, Andrei N., and Paavo Salminen. "Brownian Motion." In Handbook of Brownian Motion — Facts and Formulae. Birkhäuser Basel, 1996. http://dx.doi.org/10.1007/978-3-0348-7652-0_7.

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Dürr, Detlef, and Stefan Teufel. "Brownian motion." In Bohmian Mechanics. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/b99978_5.

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Rozanov, Yuriĭ A. "Brownian Motion." In Introduction to Random Processes. Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/978-3-642-72717-7_5.

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Bigg, Charlotte. "Brownian Motion." In Compendium of Quantum Physics. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-540-70626-7_24.

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Chow, T. S. "Brownian Motion." In Mesoscopic Physics of Complex Materials. Springer New York, 2000. http://dx.doi.org/10.1007/978-1-4612-2108-1_2.

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Koralov, Leonid, and Yakov G. Sinai. "Brownian Motion." In Theory of Probability and Random Processes. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-540-68829-7_18.

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Chorin, Alexandre J., and Ole H. Hald. "Brownian Motion." In Stochastic Tools in Mathematics and Science. Springer New York, 2009. http://dx.doi.org/10.1007/978-1-4419-1002-8_3.

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Gooch, Jan W. "Brownian Motion." In Encyclopedic Dictionary of Polymers. Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4419-6247-8_1625.

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Conference papers on the topic "Brownian motion"

1

Chandrayadula, Tarun K. "A Dyson Brownian Motion Model for Scintillation in Waveguides." In OCEANS 2024 - SINGAPORE. IEEE, 2024. http://dx.doi.org/10.1109/oceans51537.2024.10682174.

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da Silva, José Luís, and Mohamed Erraoui. "Singularity of generalized grey Brownian motion and time-changed Brownian motion." In APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 12th International On-line Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS’20. AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0029913.

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Raizen, Mark G., and Jianyong Mo. "Short-time Brownian motion." In Optical Trapping and Optical Micromanipulation XIV, edited by Kishan Dholakia and Gabriel C. Spalding. SPIE, 2017. http://dx.doi.org/10.1117/12.2275483.

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Feldorhof, B. U. "Brownian motion of suspensions." In Slow dynamics in condensed matter. AIP, 1992. http://dx.doi.org/10.1063/1.42332.

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GERHOLD, MALTE. "BI-MONOTONE BROWNIAN MOTION." In International Conference on Infinite Dimensional Analysis, Quantum Probability and Related Topics, QP38. WORLD SCIENTIFIC, 2023. http://dx.doi.org/10.1142/9789811275999_0005.

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Han, Y., A. M. Alsayed, M. Nobili, J. Zhang, T. C. Lubensky, and A. G. Yodh. "Brownian Motion of an Ellipsoid." In Laser Science. OSA, 2006. http://dx.doi.org/10.1364/ls.2006.lmh2.

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Romadani, Arista. "Brownian Motion Around Black Hole." In International Conference on Engineering, Technology and Social Science (ICONETOS 2020). Atlantis Press, 2021. http://dx.doi.org/10.2991/assehr.k.210421.061.

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Eckford, Andrew W. "Nanoscale Communication with Brownian Motion." In 2007 41st Annual Conference on Information Sciences and Systems. IEEE, 2007. http://dx.doi.org/10.1109/ciss.2007.4298292.

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LÉANDRE, RÉMI. "BROWNIAN MOTION AND CLASSIFYING SPACES." In Proceedings of the RIMS Workshop on Infinite-Dimensional Analysis and Quantum Probability. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812705242_0013.

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LÉANDRE, RÉMI. "BUNDLE GERBES AND BROWNIAN MOTION." In Proceedings of the Fifth International Workshop. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812702562_0022.

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Reports on the topic "Brownian motion"

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Adler, Robert J., and Gennady Samorodnitsky. Super Fractional Brownian Motion, Fractional Super Brownian Motion and Related Self-Similar (Super) Processes. Defense Technical Information Center, 1991. http://dx.doi.org/10.21236/ada274696.

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Adler, Robert J., and Gennady Samorodnitsky. Super Fractional Brownian Motion, Fractional Super Brownian Motion and Related Self-Similar (Super) Processes. Defense Technical Information Center, 1994. http://dx.doi.org/10.21236/ada275124.

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Tang, J. Non-Markovian quantum Brownian motion of a harmonic oscillator. Office of Scientific and Technical Information (OSTI), 1994. http://dx.doi.org/10.2172/10118416.

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Zaevski, Tsvetelin S. Laplace Transforms for the First Hitting Time of a Brownian Motion. "Prof. Marin Drinov" Publishing House of Bulgarian Academy of Sciences, 2020. http://dx.doi.org/10.7546/crabs.2020.07.05.

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Yeh, Leehwa. Quantum harmonic Brownian motion in a general environment: A modified phase-space approach. Office of Scientific and Technical Information (OSTI), 1993. http://dx.doi.org/10.2172/10194997.

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McCurdy, Keith E., Alan C. Stanton, and Wai K. Cheng. Study of Submicron Particle Size Distributions by Laser Doppler Measurement of Brownian Motion. Defense Technical Information Center, 1986. http://dx.doi.org/10.21236/ada172980.

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Соловйов, В. М., В. В. Соловйова та Д. М. Чабаненко. Динаміка параметрів α-стійкого процесу Леві для розподілів прибутковостей фінансових часових рядів. ФО-П Ткачук О. В., 2014. http://dx.doi.org/10.31812/0564/1336.

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Abstract:

Modem market economy of any country cannot successfully behave without the existence of the effective financial market. In the conditions of growing financial market, it is necessary to use modern risk-management methods, which take non-gaussian distributions into consideration. It is known, that financial and economic time series return’s distributions demonstrate so-called «heavy tails», which interrupts the modeling o f these processes with classical statistical methods. One o f the models, that is able to describe processes with «heavy tails», are the а -stable Levi processes. They can slightly simulate the dynamics of the asset prices, because it consists o f two components: the Brownian motion component and jump component. In the current work the usage of model parameters estimation procedure is proposed, which is based on the characteristic functions and is applied for the moving window for the purpose of financial-economic system’ s state monitoring.

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Duncan, Tyrone E., and Bozenna Pasik-Duncan. Optimal Control of Stochastic Systems Driven by Fractional Brownian Motions. Defense Technical Information Center, 2014. http://dx.doi.org/10.21236/ada614716.

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Zaevski, Tsvetelin N. Laplace Transforms of the Brownian Motion’s First Exit from a Strip. "Prof. Marin Drinov" Publishing House of Bulgarian Academy of Sciences, 2021. http://dx.doi.org/10.7546/crabs.2021.05.04.

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Lee, Chihoon. Constrained Stochastic Differential Equations Driven by Fractional Brownian Motions: Stationarity and Parameter Estimation Problems. Defense Technical Information Center, 2013. http://dx.doi.org/10.21236/ada591767.

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