Notes on large deviations for branching processes indexed by a Poisson process

被引：0

作者：

Gao, Zhenlong ^{[1
]}

机构：

[1] Qufu Normal Univ, Sch Stat, Qufu 273165, Shandong, Peoples R China

来源：

LITHUANIAN MATHEMATICAL JOURNAL | 2020年 / 60卷 / 01期

基金：

中国国家自然科学基金;

关键词：

branching process; Poisson process; large deviations; MODERATE DEVIATIONS; RATES;

D O I：

10.1007/s10986-020-09470-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Consider a continuous-time process {ZN(t)}, where {Z(n)} is a Galton-Watson process with offspring mean m, and {N-t} is a Poisson process independent of {Z(n)}. It turns out that R-t := ZN(t)+1/ZN(t) is an estimator of m. We deal with large deviation rates for the convergence of R-t to m for the supercritical and critical cases.

引用

页码：25 / 28

页数：4

共 15 条

[1]

[Anonymous], 2012, THESIS

[2]

Athreya K., 2012, Branching processes, Grundlehren der mathe matischen Wissenschaften

[3] LARGE DEVIATION RATES FOR BRANCHING PROCESSES-I. SINGLE TYPE CASE [J].

Athreya, K. B. .

ANNALS OF APPLIED PROBABILITY, 1994, 4 (03) :779-790

[4]

Athreya K.B., 1997, Classical and modern branching processes, V84, P1

[5]

Dembo A, 2009, Large deviations techniques and applications

[6] Stock prices as branching processes in random environments: Estimation [J].

Dion, JP ;

Epps, TW .

COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION, 1999, 28 (04) :957-975

[7]

EPPS T., 1996, Commun. Statist. Stoch. Models, V12, P529

[8] Large and moderate deviations for a renewal randomly indexed branching process [J].

Gao, Zhenlong ;

Wang, Weigang .

STATISTICS & PROBABILITY LETTERS, 2016, 116 :139-145

[9] LIMIT THEOREMS FOR A SUPERCRITICAL POISSON RANDOM INDEXED BRANCHING PROCESS [J].

Gao, Zhenlong ;

Zhang, Yanhua .

JOURNAL OF APPLIED PROBABILITY, 2016, 53 (01) :307-314

[10] Large deviations for a Poisson random indexed branching process [J].

Gao, Zhenlong ;

Wang, Weigang .

STATISTICS & PROBABILITY LETTERS, 2015, 105 :143-148

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