Integro-local limit theorems for supercritical branching process in a random environment

被引：2

作者：

Struleva, M. A. ^{[1
]}

Prokopenko, E. I. ^{[1
]}

机构：

[1] Sobolev Inst Math, Novosibirsk, Russia

来源：

STATISTICS & PROBABILITY LETTERS | 2022年 / 181卷

基金：

俄罗斯基础研究基金会;

关键词：

Large deviations; Branching process; Random environment; Light tail distribution; LARGE DEVIATIONS;

D O I：

10.1016/j.spl.2021.109234

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Let (Zn) be a supercritical branching process in a random environment (BPRE). Under certain moment assumptions, we present the precise asymptotics for the "integro-local"probabilities P(log Z(n) E [x(n), x(n) + Lambda(n))), where Lambda(n) -> 0 and x(n) -> infinity as n -> infinity. In particular, this implies the large deviations tail asymptotics for P(log Z(n) > x(n)) as n -> infinity. Like in previous research, we can see that, in the light-tail case, the main term in the large deviations asymptotics for the BPRE is provided by the associated random walk. (C) 2021 Elsevier B.V. All rights reserved.

引用

页数：9

共 18 条

[1] BRANCHING PROCESSES WITH RANDOM ENVIRONMENTS .1. EXTINCTION PROBABILITIES [J].

ATHREYA, KB ;

KARLIN, S .

ANNALS OF MATHEMATICAL STATISTICS, 1971, 42 (05) :1499-+

[2] BRANCHING PROCESSES WITH RANDOM ENVIRONMENTS, II - LIMIT THEOREMS [J].

ATHREYA, KB ;

KARLIN, S .

ANNALS OF MATHEMATICAL STATISTICS, 1971, 42 (06) :1843-+

[3]

Bansaye V., 2009, Markov Process. Related Fields, V15, P493, DOI DOI 10.48550/ARXIV.0810.4991

[4] Lower large deviations for supercritical branching processes in random environment [J].

Bansaye, Vincent ;

Boinghoff, Christian .

PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 2013, 282 (01) :15-34

[5] Upper large deviations for Branching Processes in Random Environment with heavy tails [J].

Bansaye, Vincent ;

Boeinghoff, Christian .

ELECTRONIC JOURNAL OF PROBABILITY, 2011, 16 :1900-1933

[6]

Borovkov A.A., 2013, Probability Theory, P733, DOI DOI 10.1007/978-1-4471-5201-9

[7]

Borovkov AA., 2020, ASYMPTOTIC ANAL RAND, DOI [10.1017/9781139871303, DOI 10.1017/9781139871303]

[8]

Dembo A., 2010, LARGE DEVIATIONS TEC, P308

[9]

Feller W., 1991, An Introduction to Probability Theory and its Applications, VII, P704

[10] Berry Esseen's bound and Cramer's large deviation expansion for a supercritical branching process in a random environment [J].

Grama, Ion ;

Liu, Quansheng ;

Miqueu, Eric .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2017, 127 (04) :1255-1281

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