Persistence of heavy-tailed sample averages: principle of infinitely many big jumps
Electronic Journal of Probability , Volume 27 p. 1- 25
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.
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|Electronic Journal of Probability|
|Organisation||Centrum Wiskunde & Informatica, Amsterdam (CWI), The Netherlands|
Bhattacharya, A, Palmowski, Z, & Zwart, A.P. (2022). Persistence of heavy-tailed sample averages: principle of infinitely many big jumps. Electronic Journal of Probability, 27, 1–25. doi:10.1214/22-EJP774