The Probability of Reaching a Receding Boundary by a Branching Random Walk with Fading Branching and Heavy-Tailed Jump Distribution

The Probability of Reaching a Receding Boundary by a Branching Random Walk with Fading Branching and Heavy-Tailed Jump Distribution Full article

Journal

Proceedings of the Steklov Institute of Mathematics
ISSN: 0081-5438 , E-ISSN: 1531-8605

Output data

Year: 2022, Volume: 316, Number: 1, Pages: 318-335 Pages count : 18 DOI: 10.1134/S0081543822010229

Tags

branching random walk; principle of a single big jump; receding boundary; subexponential and strong subexponential distributions

Authors

Tesemnivkov P.I. ^1,2,3 , Foss S.G. ^2,3,4

Affiliations

1	Mathematical Center in Akademgorodok, ul. Pirogova 1, Novosibirsk, 630090, Russian Federation
2	Novosibirsk State University, ul. Pirogova 1, Novosibirsk, 630090, Russian Federation
3	Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russian Federation
4	Heriot–Watt University, Edinburgh, EH14 4AS, United Kingdom

Funding (1)

Russian Science Foundation

17-11-01173

Abstract: Foss and Zachary (2003) and Foss, Palmowski and Zachary (2005) studied the probability of achieving a receding boundary on a time interval of random length by a random walk with a heavy-tailed jump distribution. They have proposed and developed a new approach that allows one to generalise the results of Asmussen (1998) to the case of arbitrary stopping times and to a wide class of nonlinear boundaries, and to obtain uniform results over all stopping times. In this paper, we consider a class of branching random walks with fading branching and obtain results on the tail asymptotics for the maximum of a branching random walk on a time interval of random (possibly unlimited) length, as well as uniform results within a class of bounded random time intervals.

Tesemnivkov P.I. , Foss S.G.
The Probability of Reaching a Receding Boundary by a Branching Random Walk with Fading Branching and Heavy-Tailed Jump Distribution
Proceedings of the Steklov Institute of Mathematics. 2022. V.316. N1. P.318-335. DOI: 10.1134/S0081543822010229 WOS Scopus РИНЦ OpenAlex

Тесемников П.И. , Фосс С.Г.
Вероятность достижения удаляющейся границы ветвящимся случайным блужданием с затуханием ветвления и тяжелым хвостом распределения скачков
Труды Математического института имени В.А. Стеклова. 2022. Т.316. С.336-354. DOI: 10.4213/tm4237 РИНЦ OpenAlex

Web of science:	WOS:000789010000022
Scopus:	2-s2.0-85129065009
Elibrary:	48432048
OpenAlex:	W3207515372

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