Fokker Planck Kolmogorov Equations


Fokker Planck Kolmogorov Equations
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Fokker Planck Kolmogorov Equations


Fokker Planck Kolmogorov Equations
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Author : Vladimir I. Bogachev
language : en
Publisher: American Mathematical Society
Release Date : 2022-02-10

Fokker Planck Kolmogorov Equations written by Vladimir I. Bogachev and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-10 with Mathematics categories.


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.



Fokker Planck Kolmogorov Equations


Fokker Planck Kolmogorov Equations
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Author :
language : en
Publisher:
Release Date : 2015

Fokker Planck Kolmogorov Equations written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Fokker-Planck equation categories.




Beyond The Triangle Brownian Motion Ito Calculus And Fokker Planck Equation Fractional Generalizations


Beyond The Triangle Brownian Motion Ito Calculus And Fokker Planck Equation Fractional Generalizations
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Author : Sabir Umarov
language : en
Publisher: World Scientific
Release Date : 2018-02-13

Beyond The Triangle Brownian Motion Ito Calculus And Fokker Planck Equation Fractional Generalizations written by Sabir Umarov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-13 with Mathematics categories.


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.



Nonlinear Fokker Planck Equations


Nonlinear Fokker Planck Equations
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Author : T.D. Frank
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-08

Nonlinear Fokker Planck Equations written by T.D. Frank and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-08 with Science categories.


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.



Beyond The Triangle


Beyond The Triangle
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Author : Sabir Umarov
language : en
Publisher:
Release Date : 2017

Beyond The Triangle written by Sabir Umarov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with MATHEMATICS categories.




Langevin And Fokker Planck Equations And Their Generalizations Descriptions And Solutions


Langevin And Fokker Planck Equations And Their Generalizations Descriptions And Solutions
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Author : Kwok Sau Fa
language : en
Publisher: World Scientific
Release Date : 2018-03-06

Langevin And Fokker Planck Equations And Their Generalizations Descriptions And Solutions written by Kwok Sau Fa and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-06 with Science categories.


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



Stochastic Processes And Applications


Stochastic Processes And Applications
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Author : Grigorios A. Pavliotis
language : en
Publisher: Springer
Release Date : 2014-11-19

Stochastic Processes And Applications written by Grigorios A. Pavliotis and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-19 with Mathematics categories.


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.



The Fokker Planck Equation For Stochastic Dynamical Systems And Its Explicit Steady State Solutions


The Fokker Planck Equation For Stochastic Dynamical Systems And Its Explicit Steady State Solutions
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Author : C Soize
language : en
Publisher: World Scientific
Release Date : 1994-05-16

The Fokker Planck Equation For Stochastic Dynamical Systems And Its Explicit Steady State Solutions written by C Soize and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-05-16 with Mathematics categories.


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



The Fokker Planck Equation


The Fokker Planck Equation
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Author : Hannes Risken
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

The Fokker Planck Equation written by Hannes Risken and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.


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.



Pde Models For Multi Agent Phenomena


Pde Models For Multi Agent Phenomena
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Author : Pierre Cardaliaguet
language : en
Publisher: Springer
Release Date : 2018-12-22

Pde Models For Multi Agent Phenomena written by Pierre Cardaliaguet and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-22 with Mathematics categories.


This volume covers selected topics addressed and discussed during the workshop “PDE models for multi-agent phenomena,” which was held in Rome, Italy, from November 28th to December 2nd, 2016. The content mainly focuses on kinetic equations and mean field games, which provide a solid framework for the description of multi-agent phenomena. The book includes original contributions on the theoretical and numerical study of the MFG system: the uniqueness issue and finite difference methods for the MFG system, MFG with state constraints, and application of MFG to market competition. The book also presents new contributions on the analysis and numerical approximation of the Fokker-Planck-Kolmogorov equations, the isotropic Landau model, the dynamical approach to the quantization problem and the asymptotic methods for fully nonlinear elliptic equations. Chiefly intended for researchers interested in the mathematical modeling of collective phenomena, the book provides an essential overview of recent advances in the field and outlines future research directions.