Skip to main content
SpringerLink
Log in
Birkhäuser
Book cover

Handbook of Brownian Motion - Facts and Formulae

  • Book
  • © 2002

Overview

Authors:
  1. Andrei N. Borodin

    1. Steklov Mathematical Institute, St. Petersburg, Russia
      Department of Mathematics and Mechanics, St. Petersburg State University, St. Petersburg, Russia

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Paavo Salminen

    1. Faculty of Science and Engineering Mathematics and Statistics, Åbo Akademi University, Turku, Finland

    View author publications

    You can also search for this author in PubMed   Google Scholar

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

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 189.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 249.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 249.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (21 chapters)

  1. Front Matter

    Pages i-xvi
    Download chapter PDF

  2. Chapter 1 Stochastic Processes in General

    • Andrei N. Borodin, Paavo Salminen
    Pages 1-11

  3. Chapter 2 Linear Diffusions

    • Andrei N. Borodin, Paavo Salminen
    Pages 12-38

  4. Chapter 3 Stochastic Calculus

    • Andrei N. Borodin, Paavo Salminen
    Pages 39-52

  5. Chapter 4 Brownian Motion

    • Andrei N. Borodin, Paavo Salminen
    Pages 53-83

  6. Chapter 5 Local Time as a Markov Process

    • Andrei N. Borodin, Paavo Salminen
    Pages 84-105

  7. Chapter 6 Differential Systems Associated to Brownian Motion

    • Andrei N. Borodin, Paavo Salminen
    Pages 106-148

  8. Introduction

    • Andrei N. Borodin, Paavo Salminen
    Pages 151-158

  9. 1. Brownian Motion

    • Andrei N. Borodin, Paavo Salminen
    Pages 159-255

  10. 2. Brownian Motion with Drift

    • Andrei N. Borodin, Paavo Salminen
    Pages 256-338

  11. 3. Reflecting Brownian Motion

    • Andrei N. Borodin, Paavo Salminen
    Pages 339-378

  12. 4. Bessel Process of Order ע

    • Andrei N. Borodin, Paavo Salminen
    Pages 379-434

  13. 5. Bessel Process of Order 1/2

    • Andrei N. Borodin, Paavo Salminen
    Pages 435-512

  14. 6. Bessel Process of Order Zero

    • Andrei N. Borodin, Paavo Salminen
    Pages 513-527

  15. 7. Ornstein–Uhlenbeck Process

    • Andrei N. Borodin, Paavo Salminen
    Pages 528-570

  16. 8. Radial Ornstein–Uhlenbeck Process

    • Andrei N. Borodin, Paavo Salminen
    Pages 571-611

  17. 9. Geometric Brownian Motion

    • Andrei N. Borodin, Paavo Salminen
    Pages 612-670

  18. Geometric Brownian Motion

    • Andrei N. Borodin, Paavo Salminen
    Pages 606-636

  19. Special Functions

    • Andrei N. Borodin, Paavo Salminen
    Pages 637-648

  20. Inverse Laplace Transforms

    • Andrei N. Borodin, Paavo Salminen
    Pages 649-651
Back to top

Keywords

About this book

There are two parts in this book. The first part is devoted mainly to the proper­ ties of linear diffusions in general and Brownian motion in particular. The second part consists of tables of distributions of functionals of Brownian motion and re­ lated processes. The primary aim of this book is to give an easy reference to a large number of facts and formulae associated to Brownian motion. We have tried to do this in a "handbook-style". By this we mean that results are given without proofs but are equipped with a reference where a proof or a derivation can be found. It is our belief and experience that such a material would be very much welcome by students and people working with applications of diffusions and Brownian motion. In discussions with many of our colleagues we have found that they share this point of view. Our original plan included more things than we were able to realize. It turned out very soon when trying to put the plan into practice that the material would be too wide to be published under one cover. Excursion theory, which most of the recent results concerning linear Brownian motion and diffusions can be classified as, is only touched upon slightly here, not to mention Brownian motion in several dimensions which enters only through the discussion of Bessel processes. On the other hand, much attention is given to the theory of local time.

Authors and Affiliations

  • Steklov Mathematical Institute, St. Petersburg, Russia

    Andrei N. Borodin

  • Department of Mathematics and Mechanics, St. Petersburg State University, St. Petersburg, Russia

    Andrei N. Borodin

  • Faculty of Science and Engineering Mathematics and Statistics, Åbo Akademi University, Turku, Finland

    Paavo Salminen

Bibliographic Information

  • Book Title: Handbook of Brownian Motion - Facts and Formulae

  • Authors: Andrei N. Borodin, Paavo Salminen

  • Series Title: Probability and Its Applications

  • DOI: https://doi.org/10.1007/978-3-0348-8163-0

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkhäuser Verlag 2002

  • Hardcover ISBN: 978-3-7643-6705-3Published: 01 May 2002

  • Softcover ISBN: 978-3-0348-9462-3Published: 23 October 2012

  • eBook ISBN: 978-3-0348-8163-0Published: 06 December 2012

  • Series ISSN: 2297-0371

  • Series E-ISSN: 2297-0398

  • Edition Number: 2

  • Number of Pages: XVI, 685

  • Topics: Probability Theory and Stochastic Processes

Publish with us

Policies and ethics

Back to top

Search

Navigation