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Macmillan Higher Education Palgrave Higher Education

Stochastic Processes and Applications

Diffusion Processes, the Fokker-Planck and Langevin Equations

ISBN 9781493913220
Publication Date December 2014
Formats Hardcover Paperback Ebook 
Publisher Springer

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.

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.

Stochastic Processes
Diffusion Processes
Introduction to Stochastic Differential Equations
The Fokker-Planck Equation
Modelling with Stochastic Differential Equations
The Langevin Equation
Exit Problems for Diffusions
Derivation of the Langevin Equation
Linear Response Theory
Appendix A Frequently Used Notations
Appendix B Elements of Probability Theory.

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
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