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Handbook of Brownian Motion — Facts and Formulae

  • Andrei N. Borodin
  • Paavo Salminen

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

  • Andrei N. Borodin
    • 1
  • Paavo Salminen
    • 2
  1. 1.St. Petersburg DivisionSteklov Mathematical InstituteSt. PetersburgRussia
  2. 2.Mathematical InstituteÅbo Akademi UniversityTurkuFinland

Bibliographic information