Probabilistic Applications of Tauberian Theorems

Yakimiv A.L.

Yakimiv (Steklov Institute of Mathematics) introduces Tauberian theorems and applies them to analyzing the asymptotic behavior of stochastic processes, record processes, random permutations, and infinitely divisible random variables. In particular, the book covers multidimensional extensions of Tauberian theorems due to Karamata, weakly oscillating functions, one-dimensional Tauberian theorems, Tauberian theorems due to Drozhzhinov and Zavyalov, Markov branching processes, and probabilities of large deviations in the context of the record model

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Table of contents :
Contents……Page 6
Introduction……Page 8
1. Tauberian theorems……Page 10
2. Applications to branching processes……Page 98
3. Random A-permutations……Page 120
4. Infinitely divisible distributions……Page 176
5. Limit theorems in the record model……Page 206
Bibliography……Page 220
Index……Page 234