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Some applications of Tauberian theorems in probability theory. (Russian) Zbl 1027.40006

This is a survey of the author’s results related to Abelian and Tauberian theorems and their applications, published during the last twenty years. The first part of the paper contains theorems of Abelian and Tauberian type and the second part contains their application to various probabilistic problems: limit theorems for the Bellman-Harris branching processes, limit theorems for some classes of random permutations, the asymptotic behavior of the record processes and probabilities of large deviations for infinitely divisible random variables. An extensive bibliography of 65 items is given too.

MSC:

40E05 Tauberian theorems
60-02 Research exposition (monographs, survey articles) pertaining to probability theory
40-02 Research exposition (monographs, survey articles) pertaining to sequences, series, summability
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