Precise Asymptotics in Limit Theorems for a Supercritical Branching Process with Immigration in a Random Environment

Chun Mao Huang; Rui Zhang; Zhi Qiang Gao

doi:10.1007/s10114-024-2493-7

Precise Asymptotics in Limit Theorems for a Supercritical Branching Process with Immigration in a Random Environment

Chun Mao Huang^*
, Rui Zhang
, Zhi Qiang Gao

^*Corresponding author for this work

Harbin Institute of Technology Weihai
Beijing Normal University

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Let (Z_n) be a supercritical branching process with immigration in an independent and identically distributed random environment. Under necessary moment conditions, we show the exact convergence rate in the central limit theorem on log Z_n and establish the corresponding local limit theorem by using the moments of the natural submartingale and the convergence rates of its logarithm. By similar approach and with the help of a change of measure, we also present the so-called integrolocal theorem and integral large deviation theorem to characterize the precise asymptotics of the upper large deviations.

Original language	English
Pages (from-to)	1850-1874
Number of pages	25
Journal	Acta Mathematica Sinica, English Series
Volume	40
Issue number	8
DOIs	https://doi.org/10.1007/s10114-024-2493-7
State	Published - Aug 2024
Externally published	Yes

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 10 Reduced Inequalities

Keywords

60F05
60F10
60J80
60K37
Branching process with immigration
central limit theorem
large deviation
random environment

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10.1007/s10114-024-2493-7

Cite this

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title = "Precise Asymptotics in Limit Theorems for a Supercritical Branching Process with Immigration in a Random Environment",

abstract = "Let (Zn) be a supercritical branching process with immigration in an independent and identically distributed random environment. Under necessary moment conditions, we show the exact convergence rate in the central limit theorem on log Zn and establish the corresponding local limit theorem by using the moments of the natural submartingale and the convergence rates of its logarithm. By similar approach and with the help of a change of measure, we also present the so-called integrolocal theorem and integral large deviation theorem to characterize the precise asymptotics of the upper large deviations.",

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author = "Huang, \{Chun Mao\} and Rui Zhang and Gao, \{Zhi Qiang\}",

note = "Publisher Copyright: {\textcopyright} Springer-Verlag GmbH Germany \& The Editorial Office of AMS 2024.",

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doi = "10.1007/s10114-024-2493-7",

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T1 - Precise Asymptotics in Limit Theorems for a Supercritical Branching Process with Immigration in a Random Environment

AU - Huang, Chun Mao

AU - Zhang, Rui

AU - Gao, Zhi Qiang

N1 - Publisher Copyright: © Springer-Verlag GmbH Germany & The Editorial Office of AMS 2024.

PY - 2024/8

Y1 - 2024/8

N2 - Let (Zn) be a supercritical branching process with immigration in an independent and identically distributed random environment. Under necessary moment conditions, we show the exact convergence rate in the central limit theorem on log Zn and establish the corresponding local limit theorem by using the moments of the natural submartingale and the convergence rates of its logarithm. By similar approach and with the help of a change of measure, we also present the so-called integrolocal theorem and integral large deviation theorem to characterize the precise asymptotics of the upper large deviations.

AB - Let (Zn) be a supercritical branching process with immigration in an independent and identically distributed random environment. Under necessary moment conditions, we show the exact convergence rate in the central limit theorem on log Zn and establish the corresponding local limit theorem by using the moments of the natural submartingale and the convergence rates of its logarithm. By similar approach and with the help of a change of measure, we also present the so-called integrolocal theorem and integral large deviation theorem to characterize the precise asymptotics of the upper large deviations.

KW - 60F05

KW - 60F10

KW - 60J80

KW - 60K37

KW - Branching process with immigration

KW - central limit theorem

KW - large deviation

KW - random environment

UR - https://www.scopus.com/pages/publications/85193407953

U2 - 10.1007/s10114-024-2493-7

DO - 10.1007/s10114-024-2493-7

M3 - 文章

AN - SCOPUS:85193407953

SN - 1439-8516

VL - 40

SP - 1850

EP - 1874

JO - Acta Mathematica Sinica, English Series

JF - Acta Mathematica Sinica, English Series

IS - 8

ER -

Precise Asymptotics in Limit Theorems for a Supercritical Branching Process with Immigration in a Random Environment

Abstract

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Keywords

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