Overview
- 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
Part of the book series: Texts in Applied Mathematics (TAM, volume 60)
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Table of contents (9 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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 toequilibrium 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.
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
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Stochastic Processes and Applications
Book Subtitle: Diffusion Processes, the Fokker-Planck and Langevin Equations
Authors: Grigorios A. Pavliotis
Series Title: Texts in Applied Mathematics
DOI: https://doi.org/10.1007/978-1-4939-1323-7
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media, LLC, part of Springer Nature 2014
Hardcover ISBN: 978-1-4939-1322-0Published: 19 November 2014
Softcover ISBN: 978-1-4939-5479-7Published: 23 August 2016
eBook ISBN: 978-1-4939-1323-7Published: 19 November 2014
Series ISSN: 0939-2475
Series E-ISSN: 2196-9949
Edition Number: 1
Number of Pages: XIII, 339
Number of Illustrations: 6 b/w illustrations, 23 illustrations in colour
Topics: Probability Theory and Stochastic Processes, Partial Differential Equations, Theoretical and Applied Mechanics, Theoretical, Mathematical and Computational Physics