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Persistence of heavy-tailed sample averages: principle of infinitely many big jumps<sup>*</sup>
Journal
Electronic Journal of Probability
Date Issued
2022-01-01
Author(s)
Bhattacharya, Ayan
Palmowski, Zbigniew
Zwart, Bert
Abstract
We consider the sample average of a centered random walk in Rd 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.
Subjects