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Stochastic Processes

  • Book
  • © 2017

Overview

Authors:
  1. Andrei N Borodin

    1. Institute of Mathematics, St. Petersburg Department of V.A.Steklov, St. Petersburg, Russia

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  • 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
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xiv
    Download chapter PDF

  2. Basic Facts

    • Andrei N. Borodin
    Pages 1-84

  3. Stochastic Calculus

    • Andrei N. Borodin
    Pages 85-196

  4. Distributions of Functionals of Brownian Motion

    • Andrei N. Borodin
    Pages 197-266

  5. Diffusion Processes

    • Andrei N. Borodin
    Pages 267-358

  6. Brownian Local Time

    • Andrei N. Borodin
    Pages 359-438

  7. Diffusions with Jumps

    • Andrei N. Borodin
    Pages 439-500

  8. Invariance Principle for Random Walks and Local Times

    • Andrei N. Borodin
    Pages 501-582

  9. Back Matter

    Pages 583-626
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Keywords

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.

 

Reviews

“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)

Authors and Affiliations

  • Institute of Mathematics, St. Petersburg Department of V.A.Steklov, St. Petersburg, Russia

    Andrei N Borodin

Bibliographic Information

  • Book Title: Stochastic Processes

  • Authors: Andrei N Borodin

  • Series Title: Probability and Its Applications

  • DOI: https://doi.org/10.1007/978-3-319-62310-8

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing AG 2017

  • Hardcover ISBN: 978-3-319-62309-2Published: 10 November 2017

  • Softcover ISBN: 978-3-319-87287-2Published: 24 May 2018

  • eBook ISBN: 978-3-319-62310-8Published: 30 October 2017

  • Series ISSN: 2297-0371

  • Series E-ISSN: 2297-0398

  • Edition Number: 1

  • Number of Pages: XIV, 626

  • Number of Illustrations: 1 b/w illustrations

  • Additional Information: Original Russian edition published by LAN Publishing, St. Petersburg, 2013

  • Topics: Probability Theory and Stochastic Processes

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