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© 1996

Handbook of Brownian Motion — Facts and Formulae

Book

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

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Theory

    1. Andrei N. Borodin, Paavo Salminen
      Pages 1-11
    2. Andrei N. Borodin, Paavo Salminen
      Pages 12-36
    3. Andrei N. Borodin, Paavo Salminen
      Pages 37-47
    4. Andrei N. Borodin, Paavo Salminen
      Pages 48-70
    5. Andrei N. Borodin, Paavo Salminen
      Pages 71-87
    6. Andrei N. Borodin, Paavo Salminen
      Pages 88-101
  3. Tables of Distributions of Functionals of Brownian Motion and Related Processes

    1. Front Matter
      Pages 120-124
    2. Andrei N. Borodin, Paavo Salminen
      Pages 125-196
    3. Andrei N. Borodin, Paavo Salminen
      Pages 197-249
    4. Andrei N. Borodin, Paavo Salminen
      Pages 250-279
    5. Andrei N. Borodin, Paavo Salminen
      Pages 280-316
    6. Andrei N. Borodin, Paavo Salminen
      Pages 317-368
    7. Andrei N. Borodin, Paavo Salminen
      Pages 369-411
    8. Andrei N. Borodin, Paavo Salminen
      Pages 412-448
  4. Back Matter
    Pages 454-465

About this book

Introduction

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.

Keywords

Bessel process Brownian motion Fusion derivation distribution form function functional local time proof stochastic processes time

Authors and affiliations

  1. 1.St. Petersburg DivisionSteklov Mathematical InstituteSt. PetersburgRussia
  2. 2.Mathematical InstituteÅbo Akademi UniversityTurkuFinland

Bibliographic information

  • Book Title Handbook of Brownian Motion — Facts and Formulae
  • Authors Andrei Borodin
    Paavo Salminen
  • Series Title Probability and Its Applications
  • DOI https://doi.org/10.1007/978-3-0348-7652-0
  • Copyright Information Birkhäuser Basel 1996
  • Publisher Name Birkhäuser, Basel
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-3-7643-5463-3
  • Softcover ISBN 978-3-0348-7654-4
  • eBook ISBN 978-3-0348-7652-0
  • Edition Number 1
  • Number of Pages XIV, 465
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Applications of Mathematics
  • Buy this book on publisher's site

Reviews

"This is an extremely useful handbook, written in the best tradition of old-fashioned scholarship... precise definitions, precisely stated results and intuitively clear explanantions... The systematic presentation...is very logical... the TeX typesetting...is pleasing to the eye throughout. The handbook is a very great service to the mathematical and scientific community."

--Mathematical Reviews