Probability theory and mathematical statistics

On asymptotics of distribution of the sojourn time on a half-axis of a random walk with heavy tails

A. S. Tarasenko<sup>ab

a</sup> Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
^b Novosibirsk State University, str. Pirogova, 2, 630090, Novosibirsk, Russia

Abstract: We study asymptotic behavior of the distribution of the sojourn time of a random walk over growing level. We assume here regular variation of the right tail distribution of summands and existence of the second moment. Some two-sided asymptotic bounds for the sojourn time distribution are established.

Keywords: random walk, sojourn time, asymptotic analysis.

UDC: 519.21

MSC: 60F10

Received November 30, 2018, published December 28, 2018

DOI: 10.3048/semi.2018.15.145

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