Chapter 1. Asymptotic Behavior of Extreme Values of Random Variables and Some Stochastic Processes


Kateryna Akbash¹ and Ivan Matsak²
¹Volodymyr Vynnychenko Central Ukrainian State Pedagogical University,
Kropyvnytsky, Ukraine
²Taras Shevchenko National University of Kyiv, Ukraine

Part of the Book: Stochastic Processes: Fundamentals and Emerging Applications

Chapter DOI:


This chapter presents a review of studies of the almost sure asymptotic behavior of extremal values of independent identically distributed random variables and stochastic processes. The central result here is the law of the iterated logarithm for lim sup, the law of the triple logarithm for lim inf and some of its refinements. Among random processes, regenerative processes, birth and death processes, and processes in queuing systems are considered.

Keywords: random variables, extreme values, limit theorems almost sure, regenerative
process, birth and death processes, queueing system


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