Large deviations for sums associated with supercritical branching process in a random environment

被引：0

作者：

Zhao, Yinxuan ^{[1
]}

Zhang, Mei ^{[1
]}

机构：

[1] Beijing Normal Univ, Sch Math Sci, Lab Math & Complex Syst, Beijing 100875, Peoples R China

来源：

STATISTICS & PROBABILITY LETTERS | 2024年 / 207卷

关键词：

Branching process; Random environment; Large deviation; Supercritical; Linear fractional; HARMONIC MOMENTS; RATES;

D O I：

10.1016/j.spl.2023.110019

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：

In this paper, we study the random sum (S)Z(n) of independent and identically distributed (i.i.d.) random variables {X-t}, where {.Z(n)} is a supercritical branching process in an i.i.d. environment.., and.. 1 is of zero mean and finite variance. We shall prove the large deviations of (S)Z(n), first in the case that.. 1 has linear fractional distribution, then in some general case.

引用

页数：13

共 10 条

[1] Large deviations for sums indexed by the generations of a Galton-Watson process [J].

Fleischmann, Klaus ;

Wachtel, Vitali .

PROBABILITY THEORY AND RELATED FIELDS, 2008, 141 (3-4) :445-470

[2] Asymptotics of the distribution and harmonic moments for a supercritical branching process in a random environment [J].

Grama, Ion ;

Liu, Quansheng ;

Miqueu, Eric .

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2023, 59 (04) :1934-1950

[3] Harmonic moments and large deviations for a supercritical branching process in a random environment [J].

Grama, Ion ;

Liu, Quansheng ;

Miqueu, Eric .

ELECTRONIC JOURNAL OF PROBABILITY, 2017, 22

[4] ON LARGE DEVIATION RATES FOR SUMS ASSOCIATED WITH GALTON-WATSON PROCESSES [J].

He, Hui .

ADVANCES IN APPLIED PROBABILITY, 2016, 48 (03) :672-690

[5]

Jacob C, 1996, CR ACAD SCI I-MATH, V322, P875

[6] Estimation of the parameters of a branching process from migrating binomial observations [J].

Jacob, C ;

Peccoud, J .

ADVANCES IN APPLIED PROBABILITY, 1998, 30 (04) :948-967

[7]

Kersting G., 2017, Discrete Time Branching Processes in Random Environment

[8] LARGE DEVIATIONS OF SUMS OF INDEPENDENT RANDOM-VARIABLES [J].

NAGAEV, SV .

ANNALS OF PROBABILITY, 1979, 7 (05) :745-789

[9]

Ney PE, 2003, ANN APPL PROBAB, V13, P475

[10] Immortal branching Markov processes: Averaging properties and PCR applications [J].

Piau, D .

ANNALS OF PROBABILITY, 2004, 32 (1A) :337-364

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