This article is cited in 1 paper

Probability theory and mathematical statistics

On a structure of a conditioned random walk on the integers with bounded local times

A. I. Sakhanenko^ab, S. G. Foss<sup>cb

a</sup> Sobolev Institute of Mathematics, Acad. Koptyug avenue, 4, 630090, Novosibirsk, Russia
^b Novosibirsk State University, Pirogova Street, 1, 630090, Novosibirsk, Russia
^c Heriot-Watt University, Riccarton Campus, EH14 4AS, Edinburgh, UK

Abstract: We consider a sample path of a random walk on the integers with bounded local times, conditioned on the event that it hits a high level. Under an auxiliary assumption, we obtain representations for its distribution in terms of the corresponding limiting sequence. Then we prove limiting results as the high level grows. In particular, we generalize results for a simple symmetric random walk obtained earlier by Benjamini and Berectycki (2010).

Keywords: random walk, bounded local times, conditioned random walk, regenerative process, potential regeneration.

UDC: 519.21

MSC: 60K37

Received September 26, 2017, published November 30, 2017

DOI: 10.17377/semi.2017.14.107

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