Texts in Applied Mathematics

Stochastic Processes and Applications

Diffusion Processes, the Fokker-Planck and Langevin Equations

Authors: Pavliotis, Grigorios A.

  • ​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
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Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-1-4939-1323-7
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.99
price for USA
  • ISBN 978-1-4939-1322-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $79.99
price for USA
  • ISBN 978-1-4939-5479-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

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.

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.

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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Table of contents (9 chapters)

  • Introduction to Stochastic Processes

    Pavliotis, Grigorios A.

    Pages 1-27

  • Diffusion Processes

    Pavliotis, Grigorios A.

    Pages 29-54

  • Introduction to Stochastic Differential Equations

    Pavliotis, Grigorios A.

    Pages 55-85

  • The Fokker–Planck Equation

    Pavliotis, Grigorios A.

    Pages 87-137

  • Modeling with Stochastic Differential Equations

    Pavliotis, Grigorios A.

    Pages 139-179

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-1-4939-1323-7
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.99
price for USA
  • ISBN 978-1-4939-1322-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $79.99
price for USA
  • ISBN 978-1-4939-5479-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Stochastic Processes and Applications
Book Subtitle
Diffusion Processes, the Fokker-Planck and Langevin Equations
Authors
Series Title
Texts in Applied Mathematics
Series Volume
60
Copyright
2014
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
Distribution Rights
Distribution rights In India: Ane Books India, New Delhi, India
eBook ISBN
978-1-4939-1323-7
DOI
10.1007/978-1-4939-1323-7
Hardcover ISBN
978-1-4939-1322-0
Softcover ISBN
978-1-4939-5479-7
Series ISSN
0939-2475
Edition Number
1
Number of Pages
XIII, 339
Number of Illustrations and Tables
6 b/w illustrations, 23 illustrations in colour
Topics