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JOURNALS // Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports] // Archive

Sib. Èlektron. Mat. Izv., 2015 Volume 12, Pages 292–299 (Mi semr586)

This article is cited in 2 papers

Probability theory and mathematical statistics

On the asymptotics of the distribution of excess

V. I. Lotovab

a Novosibirsk State University
b Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia

Abstract: We find asymptotic expansion in the powers of $e^{-b}$ for the distribution of excess over boundary $b\to\infty$ under one-sided Cramér condition on the distribution of random walk summands. As a corollary, we obtain asymptotic expansion for the renewal function.

Keywords: random walk, excess over boundary, renewal function, asymptotic expansions.

UDC: 519.21

MSC: 60G50

Received February 2, 2015, published April 28, 2015

DOI: 10.17377/semi.2015.12.023



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