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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-xvi
  2. Andrei N. Borodin, Paavo Salminen
    Pages 1-11
  3. Andrei N. Borodin, Paavo Salminen
    Pages 12-38
  4. Andrei N. Borodin, Paavo Salminen
    Pages 39-52
  5. Andrei N. Borodin, Paavo Salminen
    Pages 53-83
  6. Andrei N. Borodin, Paavo Salminen
    Pages 84-105
  7. Andrei N. Borodin, Paavo Salminen
    Pages 106-148
  8. Andrei N. Borodin, Paavo Salminen
    Pages 151-158
  9. Andrei N. Borodin, Paavo Salminen
    Pages 159-255
  10. Andrei N. Borodin, Paavo Salminen
    Pages 256-338
  11. Andrei N. Borodin, Paavo Salminen
    Pages 339-378
  12. Andrei N. Borodin, Paavo Salminen
    Pages 379-434
  13. Andrei N. Borodin, Paavo Salminen
    Pages 435-512
  14. Andrei N. Borodin, Paavo Salminen
    Pages 513-527
  15. Andrei N. Borodin, Paavo Salminen
    Pages 528-570
  16. Andrei N. Borodin, Paavo Salminen
    Pages 571-611
  17. Andrei N. Borodin, Paavo Salminen
    Pages 612-670
  18. Andrei N. Borodin, Paavo Salminen
    Pages 606-636
  19. Andrei N. Borodin, Paavo Salminen
    Pages 637-648
  20. Andrei N. Borodin, Paavo Salminen
    Pages 649-651
  21. Andrei N. Borodin, Paavo Salminen
    Pages 652-656
  22. Andrei N. Borodin, Paavo Salminen
    Pages 657-658
  23. Back Matter
    Pages 671-685

About this book

Introduction

The purpose of this book is to give an easy reference to a large number of facts and formulae associated with Brownian motion. The book consists of two parts. The first one - theory part - is devoted to properties of linear diffusions in general and Brownian motion in particular. Results are given mainly without proofs. The second one - formula part - is a table of distributions of functionals of Brownian motion and related processes. The collection contains more than 2500 numbered formulae.
This book is of value as a basic reference material to researchers, graduate students, and people doing applied work with Brownian motion and diffusions. It can also be used as a source of explicit examples when teaching stochastic processes.
Compared with the first edition published in 1996, this second edition has been revised and considerably expanded. More than 1000 new formulae have been added to the tables and, in particular, geometric Brownian motion is covered both in the theoretical and the formula part of the book.

“This is an extremely useful handbook (...) It is without any previous example in its own subject matter: the very first of its kind. The primary aim of this handbook is to serve as an easily accessible reference for an incredibly large number of facts concerning the distribution of various functionals of Brownian motion and some related stochastic processes.”

Mathematical Reviews (review of 1st edition)

"In every respect, this most reliable handbook of Brownian motion and its friends is a volume to cherish. I can highly recommend it to researchers and users of probability alike. The authors are to be congratulated on their great job in bringing all of these facts and fomulas together."

Journal of the American Statistical Association (review of 1st edition)

Keywords

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

Authors and affiliations

  • Andrei N. Borodin
    • 1
    • 2
  • Paavo Salminen
    • 3
  1. 1.Steklov Mathematical InstituteSt. PetersburgRussia
  2. 2.Department of Mathematics and MechanicsSt. Petersburg State UniversitySt. PetersburgRussia
  3. 3.Faculty of Science and Engineering Mathematics and StatisticsÅbo Akademi UniversityTurkuFinland

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-0348-8163-0
  • Copyright Information Birkhäuser Verlag 2002
  • Publisher Name Birkhäuser, Basel
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-7643-6705-3
  • Online ISBN 978-3-0348-8163-0
  • Series Print ISSN 2297-0371
  • Series Online ISSN 2297-0398
  • Buy this book on publisher's site