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

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The Probability of Reaching a Receding Boundary by a Branching Random Walk with Fading Branching and Heavy-Tailed Jump Distribution. / Tesemnivkov, P. I.; Foss, S. G.

в: Proceedings of the Steklov Institute of Mathematics, Том 316, № 1, 03.2022, стр. 318-335.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{fac486d49aa8407c902e601536405dc8,

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

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.",

keywords = "branching random walk, principle of a single big jump, receding boundary, subexponential and strong subexponential distributions",

author = "Tesemnivkov, {P. I.} and Foss, {S. G.}",

note = "Funding Information: This work is supported by the Russian Science Foundation under grant 17-11-01173-extension. Publisher Copyright: {\textcopyright} 2022, Pleiades Publishing, Ltd.",

year = "2022",

month = mar,

doi = "10.1134/S0081543822010229",

language = "English",

volume = "316",

pages = "318--335",

journal = "Proceedings of the Steklov Institute of Mathematics",

issn = "0081-5438",

publisher = "Maik Nauka Publishing / Springer SBM",

number = "1",

}

RIS

TY - JOUR

T1 - The Probability of Reaching a Receding Boundary by a Branching Random Walk with Fading Branching and Heavy-Tailed Jump Distribution

AU - Tesemnivkov, P. I.

AU - Foss, S. G.

PY - 2022/3

Y1 - 2022/3

N2 - 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.

AB - 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.

KW - branching random walk

KW - principle of a single big jump

KW - receding boundary

KW - subexponential and strong subexponential distributions

UR - http://www.scopus.com/inward/record.url?scp=85129065009&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/aa9f2347-fc45-3334-ac9b-d091bf5cdae6/

U2 - 10.1134/S0081543822010229

DO - 10.1134/S0081543822010229

M3 - Article

AN - SCOPUS:85129065009

VL - 316

SP - 318

EP - 335

JO - Proceedings of the Steklov Institute of Mathematics

JF - Proceedings of the Steklov Institute of Mathematics

SN - 0081-5438

IS - 1

ER -

ID: 36037335