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Asymptotic methods in the theory of Gaussian processes and fields. Transl. from the Russian by V. V. Piterbarg. Transl. ed. by Simeon Ivanov. (English) Zbl 0841.60024
Translations of Mathematical Monographs. 148. Providence, RI: AMS. xii, 206 p. (1996).
[For the review of the Russian original (1988) see Zbl 0652.60045.]
The book is devoted to the systematic analysis of the asymptotic behavior of distributions for various typical functionals of Gaussian random processes and fields. In particular the asymptotic behavior of \(P(\sup_{t \in T} X(t) > u)\) as \(u \to \infty\) is investigated for a class of Gaussian and similar processes. Asymptotic expansions of probabilities of high excursion of Gaussian fields and limit theorems for the number of high excursions are also given. Special attention is paid to the development of asymptotical analysis methods (the method of comparison, the double sum method, the method of moments). Both, specialists in the theory of random processes and fields and scientists working in related areas that utilize this theory will no doubt find a great deal of new and useful information in this excellent book.
Reviewer: N.Leonenko (Kiev)

MSC:
60G15 Gaussian processes
60-02 Research exposition (monographs, survey articles) pertaining to probability theory
60G60 Random fields
60G17 Sample path properties
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