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Selfsimilar processes. (English) Zbl 1008.60003
Princeton, NJ: Princeton University Press. x, 111 p. (2002).
This highly recommendable book, written by two of the leading experts on stochastic processes, provides a beautiful introduction into the growing field of selfsimilar processes. The book requires only a somewhat modest mathematical sophistication, it is thus easily accessible to a wide audience including PhD students, researchers and practitioners from finance to physics to telecommunications. After a short historical overview the book describes the current knowledge about selfsimilar processes and their applications. Topics like noncentral limit theorems and long range dependence are covered alongside statistical estimation and stochastic differential equations driven by selfsimilar processes. Particular attention is turned to selfsimilar processes with stationary increments and fractional Brownian motion (fBm). This includes stochastic integrals with respect to and the distribution of the maximum of fBm.

60-02 Research exposition (monographs, survey articles) pertaining to probability theory
60G18 Self-similar stochastic processes
60G35 Signal detection and filtering (aspects of stochastic processes)