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© 2014

Stochastic Processes and Applications

Diffusion Processes, the Fokker-Planck and Langevin Equations

Benefits

  • One of the first textbooks addressing modern stochastic methods which is addressed for the applied mathematician, scientist and engineer

  • Includes many exercises and references/links to current research topics covered in the books

  • Class tested for many years in the UK and in Germany

  • Several techniques for studying stochastic processes in continuous time are presented

Textbook

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

  1. 1.Department of Mathematics South Kensington CampusImperial College LondonLondonUnited Kingdom

About the authors

Dr. Grigorios A. Pavliotis is a professor in Applied Mathematics at the Imperial College in London. Dr. Pavliotis's research interests include analysis, numerical, and statistical inference for multiscale stochastic systems, non-equilibrium statistical mechanics, and homogenization theory for PDEs and SDEs.

Bibliographic information

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Reviews

“This is another useful book for readers with ‘normal’ knowledge in mathematics, in particular in analysis, probability and partial differential equations. The goal of the author is to describe basic techniques from the theory of stochastic processes needed to answer questions coming from natural sciences such as physics and chemistry. … The book will be accessible and useful for graduate university students and teachers of courses in applied mathematics and other natural sciences.” (Jordan M. Stoyanov, zbMATH 1318.60003, 2015)

"In the reviewer's opinion, [Stochastic Processes and Applications] could be recommended for ambitious undergraduate and standard graduate students as well as researchers who are unfamiliar with stochastic processes but eager to apply them to random phenomena, as a reference appropriate for use both as a textbook and for self-study."

Isamu Doku, review for the American Mathematical Society