A note on recurrent random walks

Dimitrios Cheliotis

Statistics & Probability Letters, 2006, vol. 76, issue 10, 1025-1031

Abstract: For any recurrent random walk (Sn)n[greater-or-equal, slanted]1 on , there are increasing sequences (gn)n[greater-or-equal, slanted]1 converging to infinity for which (gnSn)n[greater-or-equal, slanted]1 has at least one finite accumulation point. For one class of random walks, we give a criterion on (gn)n[greater-or-equal, slanted]1 and the distribution of S1 determining the set of accumulation points for (gnSn)n[greater-or-equal, slanted]1. This extends, with a simpler proof, a result of Chung and Erdös. Finally, for recurrent, symmetric random walks, we give a criterion characterizing the increasing sequences (gn)n[greater-or-equal, slanted]1 of positive numbers for which .

Keywords: Random; walk; Recurrence; Stable; distributions; Symmetric; distributions (search for similar items in EconPapers)
Date: 2006
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