Fokker Planck Kolmogorov Equations

Author : Vladimir I. Bogachev,Nicolai V. Krylov,Michael Röckner,Stanislav V. Shaposhnikov
Publisher : American Mathematical Society
Page : 495 pages
File Size : 40,5 Mb
Release : 2022-02-10
Category : Mathematics
ISBN : 9781470470098

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Fokker–Planck–Kolmogorov Equations by Vladimir I. Bogachev,Nicolai V. Krylov,Michael Röckner,Stanislav V. Shaposhnikov Pdf

This book gives an exposition of the principal concepts and results related to second order elliptic and parabolic equations for measures, the main examples of which are Fokker–Planck–Kolmogorov equations for stationary and transition probabilities of diffusion processes. Existence and uniqueness of solutions are studied along with existence and Sobolev regularity of their densities and upper and lower bounds for the latter. The target readership includes mathematicians and physicists whose research is related to diffusion processes as well as elliptic and parabolic equations.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 48,7 Mb
Release : 2015
Category : Fokker-Planck equation
ISBN : 1470427931

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Fokker-Planck-Kolmogorov equations by Anonim Pdf

Author : T.D. Frank
Publisher : Springer Science & Business Media
Page : 415 pages
File Size : 50,6 Mb
Release : 2005-12-08
Category : Science
ISBN : 9783540264774

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Nonlinear Fokker-Planck Equations by T.D. Frank Pdf

Centered around the natural phenomena of relaxations and fluctuations, this monograph provides readers with a solid foundation in the linear and nonlinear Fokker-Planck equations that describe the evolution of distribution functions. It emphasizes principles and notions of the theory (e.g. self-organization, stochastic feedback, free energy, and Markov processes), while also illustrating the wide applicability (e.g. collective behavior, multistability, front dynamics, and quantum particle distribution). The focus is on relaxation processes in homogeneous many-body systems describable by nonlinear Fokker-Planck equations. Also treated are Langevin equations and correlation functions. Since these phenomena are exhibited by a diverse spectrum of systems, examples and applications span the fields of physics, biology and neurophysics, mathematics, psychology, and biomechanics.

Author : Sabir Umarov,Marjorie Hahn,Kei Kobayashi
Publisher : World Scientific
Page : 192 pages
File Size : 54,7 Mb
Release : 2018-02-13
Category : Mathematics
ISBN : 9789813230996

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Beyond The Triangle: Brownian Motion, Ito Calculus, And Fokker-planck Equation - Fractional Generalizations by Sabir Umarov,Marjorie Hahn,Kei Kobayashi Pdf

The book is devoted to the fundamental relationship between three objects: a stochastic process, stochastic differential equations driven by that process and their associated Fokker-Planck-Kolmogorov equations. This book discusses wide fractional generalizations of this fundamental triple relationship, where the driving process represents a time-changed stochastic process; the Fokker-Planck-Kolmogorov equation involves time-fractional order derivatives and spatial pseudo-differential operators; and the associated stochastic differential equation describes the stochastic behavior of the solution process. It contains recent results obtained in this direction.This book is important since the latest developments in the field, including the role of driving processes and their scaling limits, the forms of corresponding stochastic differential equations, and associated FPK equations, are systematically presented. Examples and important applications to various scientific, engineering, and economics problems make the book attractive for all interested researchers, educators, and graduate students.

Author : Kwok Sau Fa
Publisher : World Scientific
Page : 208 pages
File Size : 45,9 Mb
Release : 2018-03-06
Category : Science
ISBN : 9789813228429

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Langevin And Fokker-planck Equations And Their Generalizations: Descriptions And Solutions by Kwok Sau Fa Pdf

This invaluable book provides a broad introduction to a rapidly growing area of nonequilibrium statistical physics. The first part of the book complements the classical book on the Langevin and Fokker–Planck equations (H. Risken, The Fokker–Planck Equation: Methods of Solution and Applications (Springer, 1996)). Some topics and methods of solutions are presented and discussed in details which are not described in Risken's book, such as the method of similarity solution, the method of characteristics, transformation of diffusion processes into the Wiener process in different prescriptions, harmonic noise and relativistic Brownian motion. Connection between the Langevin equation and Tsallis distribution is also discussed. Due to the growing interest in the research on the generalized Langevin equations, several of them are presented. They are described with some details. Recent research on the integro-differential Fokker–Planck equation derived from the continuous time random walk model shows that the topic has several aspects to be explored. This equation is worked analytically for the linear force and the generic waiting time probability distribution function. Moreover, generalized Klein-Kramers equations are also presented and discussed. They have the potential to be applied to natural systems, such as biological systems. Contents: Introduction Langevin and Fokker–Planck Equations Fokker–Planck Equation for One Variable and its Solution Fokker–Planck Equation for Several Variables Generalized Langevin Equations Continuous Time Random Walk Model Uncoupled Continuous Time Random Walk Model andits Solution Readership: Advanced undergraduate and graduate students in mathematical physics and statistical physics; biologists and chemists who are interested in nonequilibrium statistical physics. Keywords: Langevin Equation;Fokker-Planck Equation;Klein-Kramers Equation;Continuous Time Random Walk Model;Colored Noise;Tsallis Entropy;Population Growth Models;Wright Functions;Mittag-Leffler Function;Method of Similarity Solution;First Passage Time;Relativistic Brownian Motion;Fractional Derivatives;Integro-Differential Fokker-Planck EquationsReview: Key Features: This book complements Risken's book on the Langevin and Fokker-Planck equations. Some topics and methods of solutions are presented and discussed in details which are not described in Risken's book Several generalized Langevin equations are presented and discussed with some detail Integro-differential Fokker–Planck equation is derived from the uncoupled continuous time random walk model for generic waiting time probability distribution function which can be used to distinguish the differences for the initial and intermediate times with the same behavior in the long-time limit. Moreover, generalized Klein–Kramers equations are also described and discussed. To our knowledge these approaches are not found in other textbooks

Author : Hannes Risken,Till Frank
Publisher : Springer Science & Business Media
Page : 486 pages
File Size : 44,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642615443

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The Fokker-Planck Equation by Hannes Risken,Till Frank Pdf

This is the first textbook to include the matrix continued-fraction method, which is very effective in dealing with simple Fokker-Planck equations having two variables. Other methods covered are the simulation method, the eigen-function expansion, numerical integration, and the variational method. Each solution is applied to the statistics of a simple laser model and to Brownian motion in potentials. The whole is rounded off with a supplement containing a short review of new material together with some recent references. This new study edition will prove to be very useful for graduate students in physics, chemical physics, and electrical engineering, as well as for research workers in these fields.

Author : C Soize
Publisher : World Scientific
Page : 340 pages
File Size : 54,5 Mb
Release : 1994-05-16
Category : Mathematics
ISBN : 9789814502023

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The Fokker-Planck Equation for Stochastic Dynamical Systems and Its Explicit Steady State Solutions by C Soize Pdf

This is an analysis of multidimensional nonlinear dissipative Hamiltonian dynamical systems subjected to parametric and external stochastic excitations by the Fokker-Planck equation method. The author answers three types of questions concerning this area. First, what probabilistic tools are necessary for constructing a stochastic model and deriving the FKP equation for nonlinear stochastic dynamical systems? Secondly, what are the main results concerning the existence and uniqueness of an invariant measure and its associated stationary response? Finally, what is the class of multidimensional dynamical systems that have an explicit invariant measure and what are the fundamental examples for applications? Contents:Stochastic Canonical Equation of Multidimensional Nonlinear Dissipative Hamiltonian Dynamical SystemsFundamental Examples of Nonlinear Dynamical Systems and Associated Second-Order EquationBrief Review of Probability and Random VariablesProbabilistic Tools I. Classical Stochastic ProcessesProbabilistic Tools II. Mean-Square Theory of Linear Integral Transformations and of Linear Differential EquationsProbabilistic Tools III. Diffusion Processes and Fokker-Planck EquationProbabilistic Tools IV. Stochastic Integrals and Stochastic Differential EquationsStochastic Modeling with Stochastic Differential EquationsFKP Equation for the Dissipative Hamiltonian Dynamical SystemsStationary Response of Dissipative Dynamical Systems, Existence and Uniqueness, Explicit Solution of an Invariant MeasureComplements for the Normalization Condition, Characteristic Function and Moments of the Invariant MeasureApplication I. Multidimensional Linear Oscillators Subject to External and Parametric Random ExcitationsApplication II. Multidimensional Nonlinear Oscillators with Inertial Nonlinearity Subject to External Random ExcitationsApplication III. Multidimensional Nonlinear Oscillators Subject to External and Parametric Random ExcitationsSymplectic Change of Variables in the Multidimensional Unsteady FKP Equation ReferencesIndex Readership: Applied mathematicians. keywords:Fokker–Planck Equation;Stochastic Dynamics;Diffusion Process;Stochastic Methods;Random Vibration;Random Process;Stochastic Differential Equation;Hamiltonian Dynamical System;Stochastic Process;Probabilistic Methods “This is a timely volume summarizing and unifying 30 years of search for explicit solutions of (stationary) FPE's. New articles in this area, which continue to appear, have to explain in which way they extend Soize's presentation. As such, this book is a useful reference for the random vibrations community.” Mathematics Abstracts

Author : Hannes Risken,Till Frank
Publisher : Springer Science & Business Media
Page : 494 pages
File Size : 46,5 Mb
Release : 1996-09-17
Category : Mathematics
ISBN : 354061530X

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The Fokker-Planck Equation by Hannes Risken,Till Frank Pdf

This is the first textbook to include the matrix continued-fraction method, which is very effective in dealing with simple Fokker-Planck equations having two variables. Other methods covered are the simulation method, the eigen-function expansion, numerical integration, and the variational method. Each solution is applied to the statistics of a simple laser model and to Brownian motion in potentials. The whole is rounded off with a supplement containing a short review of new material together with some recent references. This new study edition will prove to be very useful for graduate students in physics, chemical physics, and electrical engineering, as well as for research workers in these fields.

Author : Sabir Umarov,Marjorie G. Hahn,Kei Kobayashi (Mathematics professor)
Publisher : Unknown
Page : 192 pages
File Size : 46,7 Mb
Release : 2017
Category : MATHEMATICS
ISBN : 9813230924

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Beyond the Triangle by Sabir Umarov,Marjorie G. Hahn,Kei Kobayashi (Mathematics professor) Pdf

Author : Stéphane Menozzi
Publisher : Springer Nature
Page : 354 pages
File Size : 50,8 Mb
Release : 2024-06-28
Category : Electronic
ISBN : 9789819702251

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Kolmogorov Operators and Their Applications by Stéphane Menozzi Pdf

Author : Grigorios A. Pavliotis
Publisher : Springer
Page : 345 pages
File Size : 50,5 Mb
Release : 2014-11-19
Category : Mathematics
ISBN : 9781493913237

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Stochastic Processes and Applications by Grigorios A. Pavliotis Pdf

This book presents various results and techniques from the theory of stochastic processes that are useful in the study of stochastic problems in the natural sciences. The main focus is analytical methods, although numerical methods and statistical inference methodologies for studying diffusion processes are also presented. The goal is the development of techniques that are applicable to a wide variety of stochastic models that appear in physics, chemistry and other natural sciences. Applications such as stochastic resonance, Brownian motion in periodic potentials and Brownian motors are studied and the connection between diffusion processes and time-dependent statistical mechanics is elucidated. The book contains a large number of illustrations, examples, and exercises. It will be useful for graduate-level courses on stochastic processes for students in applied mathematics, physics and engineering. Many of the topics covered in this book (reversible diffusions, convergence to equilibrium for diffusion processes, inference methods for stochastic differential equations, derivation of the generalized Langevin equation, exit time problems) cannot be easily found in textbook form and will be useful to both researchers and students interested in the applications of stochastic processes.

Author : Joseph L. McCauley
Publisher : Cambridge University Press
Page : 219 pages
File Size : 52,7 Mb
Release : 2013-02-21
Category : Business & Economics
ISBN : 9780521763400

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Stochastic Calculus and Differential Equations for Physics and Finance by Joseph L. McCauley Pdf

Provides graduate students and practitioners in physics and economics with a better understanding of stochastic processes.

Author : Johan Grasman,Onno A., van Herwaarden
Publisher : Springer Science & Business Media
Page : 224 pages
File Size : 51,9 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662038574

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Asymptotic Methods for the Fokker-Planck Equation and the Exit Problem in Applications by Johan Grasman,Onno A., van Herwaarden Pdf

Asymptotic methods are of great importance for practical applications, especially in dealing with boundary value problems for small stochastic perturbations. This book deals with nonlinear dynamical systems perturbed by noise. It addresses problems in which noise leads to qualitative changes, escape from the attraction domain, or extinction in population dynamics. The most likely exit point and expected escape time are determined with singular perturbation methods for the corresponding Fokker-Planck equation. The authors indicate how their techniques relate to the Itô calculus applied to the Langevin equation. The book will be useful to researchers and graduate students.

Author : William Coffey,Yu. P. Kalmykov,J. T. Waldron
Publisher : World Scientific
Page : 436 pages
File Size : 55,9 Mb
Release : 1996
Category : Mathematics
ISBN : 9810216513

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The Langevin Equation by William Coffey,Yu. P. Kalmykov,J. T. Waldron Pdf

The book is suitable for a lecture course on the theory of Brownian motion, being based on final year undergraduate lectures given at Trinity College, Dublin. Topics that are discussed include: white noise; the Chapman-Kolmogorov equation ? Kramers-Moyal expansion; the Langevin equation; the Fokker-Planck equation; Brownian motion of a free particle; spectral density and the Wiener-Khintchin theorem ? Brownian motion in a potential application to the Josephson effect, ring laser gyro; Brownian motion in two dimensions; harmonic oscillators; itinerant oscillators; linear response theory; rotational Brownian motion; application to loss processes in dielectric and ferrofluids; superparamagnetism and nonlinear relaxation processes.As the first elementary book on the Langevin equation approach to Brownian motion, this volume attempts to fill in all the missing details which students find particularly hard to comprehend from the fundamental papers contained in the Dover reprint ? Selected Papers on Noise and Stochastic Processes, ed. N Wax (1954) ? together with modern applications particularly to relaxation in ferrofluids and polar dielectrics.

Author : Werner Dubitzky,Olaf Wolkenhauer,Hiroki Yokota,Kwang-Hyun Cho
Publisher : Springer
Page : 0 pages
File Size : 54,8 Mb
Release : 2013-06-05
Category : Science
ISBN : 1441998624

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Encyclopedia of Systems Biology by Werner Dubitzky,Olaf Wolkenhauer,Hiroki Yokota,Kwang-Hyun Cho Pdf

Systems biology refers to the quantitative analysis of the dynamic interactions among several components of a biological system and aims to understand the behavior of the system as a whole. Systems biology involves the development and application of systems theory concepts for the study of complex biological systems through iteration over mathematical modeling, computational simulation and biological experimentation. Systems biology could be viewed as a tool to increase our understanding of biological systems, to develop more directed experiments, and to allow accurate predictions. The Encyclopedia of Systems Biology is conceived as a comprehensive reference work covering all aspects of systems biology, in particular the investigation of living matter involving a tight coupling of biological experimentation, mathematical modeling and computational analysis and simulation. The main goal of the Encyclopedia is to provide a complete reference of established knowledge in systems biology – a ‘one-stop shop’ for someone seeking information on key concepts of systems biology. As a result, the Encyclopedia comprises a broad range of topics relevant in the context of systems biology. The audience targeted by the Encyclopedia includes researchers, developers, teachers, students and practitioners who are interested or working in the field of systems biology. Keeping in mind the varying needs of the potential readership, we have structured and presented the content in a way that is accessible to readers from wide range of backgrounds. In contrast to encyclopedic online resources, which often rely on the general public to author their content, a key consideration in the development of the Encyclopedia of Systems Biology was to have subject matter experts define the concepts and subjects of systems biology.