This article is cited in 3 papers

Limit behavior of a simple random walk with non-integrable jump from a barrier

A. Yu. Pilipenko^a, Yu. E. Prykhodko<sup>b

a</sup> Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkivska str. 3, 01601, Kiev, Ukraine
^b NTUU "KPI", 37, Prospect Peremohy, 03056, Kyiv-56, Ukraine

Abstract: Consider a Markov chain on $\mathbb{Z}_+$ with reflecting barrier at 0 such that jumps of the chain outside of 0 are i.i.d. with mean zero and finite variance. It is assumed that the jump from 0 has a distribution that belongs to the domain of attraction of non-negative stable law. It is proved that under natural scaling of a space and a time a limit of this scaled Markov chain is a Brownian motion with some Wentzell's boundary condition at 0.

Keywords: Random walk; Wentzell's boundary condition; invariance principle.

MSC: 60F17, 60J50, 60J60

Language: English

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