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A limit theorem for extreme values of discrete random variables and its applications. (English. Ukrainian original) Zbl 1455.60049

Theory Probab. Math. Stat. 101, 217-231 (2020); translation from Teor. Jmovirn. Mat. Stat. 101, 189-202 (2019).
Summary: Almost sure asymptotic behavior of extreme values of discrete random variables is studied. Applications of the main result on the asymptotics are discussed to birth and death processes as well as to length processes describing the length of a queue in a queuing system.

MSC:

60F15 Strong limit theorems
60G70 Extreme value theory; extremal stochastic processes
60K25 Queueing theory (aspects of probability theory)
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
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