© 2017

Stochastic Processes


  • Gives a rigorous yet understandable presentation of the theory of stochastic processes

  • Presents the theory of distributions of functionals of diffusions including local times, rarely found in literature

  • Devotes serious attention to the Brownian local time

  • Includes many examples and exercises


Part of the Probability and Its Applications book series (PA)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Andrei N. Borodin
    Pages 1-84
  3. Andrei N. Borodin
    Pages 85-196
  4. Andrei N. Borodin
    Pages 197-266
  5. Andrei N. Borodin
    Pages 267-358
  6. Andrei N. Borodin
    Pages 359-438
  7. Andrei N. Borodin
    Pages 439-500
  8. Back Matter
    Pages 583-626

About this book


This book provides a rigorous yet accessible introduction to the theory of stochastic processes. A significant part of the book is devoted to the classic theory of stochastic processes. In turn, it also presents proofs of well-known results, sometimes together with new approaches. Moreover, the book explores topics not previously covered elsewhere, such as distributions of functionals of diffusions stopped at different random times, the Brownian local time, diffusions with jumps, and an invariance principle for random walks and local times.

Supported by carefully selected material, the book showcases a wealth of examples that demonstrate how to solve concrete problems by applying theoretical results. It addresses a broad range of applications, focusing on concrete computational techniques rather than on abstract theory. The content presented here is largely self-contained, making it suitable for researchers and graduate students alike.


stochastic calculus diffusion processes Brownian motion differential equations conditional probabilities conditional expectations

Authors and affiliations

  1. 1.Institute of MathematicsSt. Petersburg Department of V.A.SteklovSt. PetersburgRussia

Bibliographic information

  • Book Title Stochastic Processes
  • Authors Andrei N Borodin
  • Series Title Probability and Its Applications
  • Series Abbreviated Title Probability,its Applications
  • DOI
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-319-62309-2
  • Softcover ISBN 978-3-319-87287-2
  • eBook ISBN 978-3-319-62310-8
  • Series ISSN 2297-0371
  • Series E-ISSN 2297-0398
  • Edition Number 1
  • Number of Pages XIV, 626
  • Number of Illustrations 1 b/w illustrations, 0 illustrations in colour
  • Additional Information Original Russian edition published by LAN Publishing, St. Petersburg, 2013
  • Topics Probability Theory and Stochastic Processes
  • Buy this book on publisher's site
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“The aim of the book is to give a rigorous and at the same time accessible presentation of the theory of stochastic processes. … The book is written in a clear and rigorous language, and will be useful to students, graduate students, teachers and anyone who is interested in the theory of stochastic processes.” (Yuliya S. Mishura, zbMATH 1390.60003, 2018)