Stochastic Processes and Applications: Diffusion Processes, the Fokker-Planck and Langevin Equations

ISBN-13: 9781493954797 / Angielski / Miękka / 2016 / 339 str.

Grigorios A. Pavliotis

Opis

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.

Recenzje

"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

Spis treści

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.

O autorze

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.