Persistence of heavy-tailed sample averages: principle of infinitely many big jumps

Ayan Bhattacharya; Zbigniew Palmowski; Bert Zwart

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arXiv · 1902.09922

Persistence of heavy-tailed sample averages: principle of infinitely many big jumps

Ayan Bhattacharya·Zbigniew Palmowski·Bert Zwart

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Abstract

We consider the sample average of a centered random walk in $\mathbb{R}^d$ with regularly varying step size distribution. For the first exit time from a compact convex set $A$ not containing the origin, we show that its tail is of lognormal type. Moreover, we show that the typical way for a large exit time to occur is by having a number of jumps growing logarithmically in the scaling parameter.

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Ayan Bhattacharya, Zbigniew Palmowski, Bert Zwart. 2019-02-26. Persistence of heavy-tailed sample averages: principle of infinitely many big jumps. https://arxiv.org/abs/1902.09922

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