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

Autor:	Bhattacharya, Ayan, Palmowski, Zbigniew, Zwart, Bert
Rok vydání:	2019
Předmět:	Mathematics - Probability
Druh dokumentu:	Working Paper
Popis:	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. Comment: 30 pages, 2 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1902.09922 Zobrazit plný text záznamu View this record from Arxiv