Handbook of Brownian Motion - Facts and Formulae

1. Front Matter

   Pages i-xvi

   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

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
• Markov process
• Mathematical Finance
• Ornstein-Uhlenbeck process
• Probability
• Statistics
• Stochastic Processes
• Stochastic calculus
• calculus
• geometric Brownian motion
• local time
• stochastic process

• 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

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