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The purpose of this book is to give an easy reference to a large number of facts and formulae associated 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.
Content Level »Research
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
I: Theory.- I. Stochastic processes in general.- II. Linear diffusions.- III. Stochastic calculus.- IV. Brownian motion.- V. Local time as a Markov process.- VI. Differential systems associated to Brownian motion.- Appendix 1. Briefly on some diffusions.- II: TABLES OF DISTRIBUTIONS OF FUNCTIONALS OF BROWNIAN MOTION AND RELATED PROCESSES.- 1. Brownian motion.- 2. Brownian motion with drift.- 3. Reflecting Brownian motion.- 4. Bessel process of order ?.- 5. Bessel process of order 1/2.- 6. Bessel process of order zero.- 7. Ornstein-Uhlenbeck process.- 8. Radial Ornstein-Uhlenbeck process.- 9. Geometric Brownian motion.- Appendix 2. Special functions.- Appendix 3. Inverse Laplace transforms.- Appendix 4. Differential equations and their solutions.- Appendix 5. Formulae for n-fold differentiation.