Recurrence properties of a special type of heavy-tailed random walk

Date

2011

Journal Title

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Abstract

In the proof of the invariance principle for locally perturbed periodic Lorentz process with finite horizon, a lot of delicate results were needed concerning the recurrence properties of its unperturbed version. These were analogous to the similar properties of Simple Symmetric Random Walk. How- ever, in the case of Lorentz process with infinite horizon, the analogous results for the corresponding random walk are not known, either. In this paper, these properties are ascertained for the appropri- ate random walk (this happens to be in the non normal domain of attraction of the normal law). As a tool, an estimation of the remainder term in the local limit theorem for the corresponding random walk is computed.

Description

Scholarly article / OA (arXiv PDF)

Keywords

Random walk, Heavy tail, Recurrence, Local limit theorem

Citation

Nándori, P. (2011). Recurrence properties of a special type of heavy-tailed random walk. Journal of Statistical Physics: 1, 142(2), 342–355. https://doi-org.ezproxy.yu.edu/10.1007/s10955-010-0116-4