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Handbook of Brownian motion: Facts and formulae. 2nd ed. (English) Zbl 1012.60003
Probability and Its Applications. Basel: Birkhäuser. xvi, 672 p. (2002).
This is the second edition of a very useful book on facts and formulae about Brownian motion. (The first edition (1996) is covered by Zbl 0859.60001.) The second edition is revised and considerably expanded. In particular, there are new sections in the theory part as well as in the formula part devoted to results on geometric Brownian motion and to the Feynman-Kac formula concerning functionals stopped at first range time. The Appendix “Briefly on some diffusions” has been extended with new processes, such as radial Ornstein-Uhlenbeck processes and their squares. Three new appendices cover formulae for inverse Laplace transforms, second-order ordinary differential equations and their fundamental solutions and formulae on \(n\)-fold differentiation of the product and composition of two functions. To keep the book a reasonable size in spite of the extensions, some formulae appearing in the first book have been omitted, when they were simple consequences of others.

60-02 Research exposition (monographs, survey articles) pertaining to probability theory
60Jxx Markov processes
60J65 Brownian motion
60Gxx Stochastic processes