Handbook of Brownian Motion

1. Front Matter

   Pages i-xiv

   PDF

2. Theory

   1. Stochastic Processes in General

      • Andrei N. Borodin, Paavo Salminen

      Pages 1-11

   2. Linear Diffusions

      • Andrei N. Borodin, Paavo Salminen

      Pages 12-36

   3. Stochastic Calculus

      • Andrei N. Borodin, Paavo Salminen

      Pages 37-47

   4. Brownian Motion

      • Andrei N. Borodin, Paavo Salminen

      Pages 48-70

   5. Local Time as a Markov Process

      • Andrei N. Borodin, Paavo Salminen

      Pages 71-87

   6. Differential Systems Associated to Brownian Motion

      • 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

      PDF

   2. Brownian Motion

      • Andrei N. Borodin, Paavo Salminen

      Pages 125-196

   3. Brownian Motion with Drift

      • Andrei N. Borodin, Paavo Salminen

      Pages 197-249

   4. Reflecting Brownian Motion

      • Andrei N. Borodin, Paavo Salminen

      Pages 250-279

   5. Bessel Process of Order Zero

      • Andrei N. Borodin, Paavo Salminen

      Pages 280-316

   6. Bessel Process of Order 1/2

      • Andrei N. Borodin, Paavo Salminen

      Pages 317-368

   7. Bessel Process of Order ν > 0

      • Andrei N. Borodin, Paavo Salminen

      Pages 369-411

   8. Ornstein-Uhlenbeck Process

      • Andrei N. Borodin, Paavo Salminen

      Pages 412-448

4. Back Matter

   Pages 454-465

   PDF

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.

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

"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 

• St. Petersburg Division, Steklov Mathematical Institute, St. Petersburg, Russia

  Andrei N. Borodin

• Mathematical Institute, Åbo Akademi University, Turku, Finland

  Paavo Salminen

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