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Stochastic Processes and Applications

Diffusion Processes, the Fokker-Planck and Langevin Equations

  • Grigorios A. Pavliotis

Part of the Texts in Applied Mathematics book series (TAM, volume 60)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Grigorios A. Pavliotis
    Pages 1-27
  3. Grigorios A. Pavliotis
    Pages 29-54
  4. Grigorios A. Pavliotis
    Pages 55-85
  5. Grigorios A. Pavliotis
    Pages 87-137
  6. Grigorios A. Pavliotis
    Pages 139-179
  7. Grigorios A. Pavliotis
    Pages 181-233
  8. Grigorios A. Pavliotis
    Pages 235-266
  9. Grigorios A. Pavliotis
    Pages 267-282
  10. Grigorios A. Pavliotis
    Pages 283-296
  11. Back Matter
    Pages 297-339

About this book

Introduction

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.

Keywords

Diffusion Processes Fokker-Planck Equation Lengevin Equation Statistical Mechanics Stochastic Differential Equations Stochastic Processes

Authors and affiliations

  • Grigorios A. Pavliotis
    • 1
  1. 1.Department of Mathematics South Kensington CampusImperial College LondonLondonUnited Kingdom

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4939-1323-7
  • Copyright Information Springer Science+Business Media New York 2014
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4939-1322-0
  • Online ISBN 978-1-4939-1323-7
  • Series Print ISSN 0939-2475
  • Series Online ISSN 2196-9949
  • Buy this book on publisher's site