Abstract: We consider exit times for random walks with independent but not necessarily identically distributed increments. We are going to describe an asymptotic behavior of the probability that the random walk stays above the moving boundary for a long time. In the paper by D. Denisov, A. Sakhanenko, and V. Wachtel (Ann. Probab., 2018) an universal asymptotic formula for such probability was found in the case when the random walk satis es the classical Lindeberg condition. Now we investigate a question if it is possible to nd similar asymptotics for more general random walks when increments may have in nite variances, but the central limit theorem is still valid. We obtain such result for a class of walks with symmetrically distributed increments.

Cite: Sakhanenko A.I.
О временах первого прохождения для симметричных случайных блужданий без условия Линдеберга
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2023. Т.20. №1. С.86-99. DOI: 10.33048/semi.2023.20.008 WOS Scopus РИНЦ

Dates:

Submitted:	Nov 22, 2022
Published print:	Feb 13, 2023
Published online:	Feb 13, 2023

Identifiers:

Web of science:	WOS:000959070400002
Scopus:	2-s2.0-85150812460
Elibrary:	54768280

Citing: Пока нет цитирований

Altmetrics: