Wasserstein-1 Distance and Nonuniform Berry-Esseen Bound for a Supercritical Branching Process in a Random Environment

Hao Wu; Xiequan Fan; Zhiqiang Gao; Yinna Ye

doi:10.3770/j.issn:2095-2651.2023.06.009

Wasserstein-1 Distance and Nonuniform Berry-Esseen Bound for a Supercritical Branching Process in a Random Environment

Hao Wu
, Xiequan Fan
, Zhiqiang Gao
, Yinna Ye^*

^*Corresponding author for this work

Tianjin University
Northeastern University China
Beijing Normal University

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

Abstract

Let (Z_n)_n≥0 be a supercritical branching process in an independent and identically distributed random environment. We establish an optimal convergence rate in the Wasserstein-1 distance for the process (Z_n)_n≥0, which completes a result of Grama et al. [Stochastic Process. Appl., 2017, 127(4): 1255–1281]. Moreover, an exponential nonuniform Berry-Esseen bound is also given. At last, some applications of the main results to the confidence interval estimation for the criticality parameter and the population size Z_n are discussed.

Original language	English
Pages (from-to)	737-753
Number of pages	17
Journal	Journal of Mathematical Research with Applications
Volume	43
Issue number	6
DOIs	https://doi.org/10.3770/j.issn:2095-2651.2023.06.009
Publication status	Published - 2023

Keywords

Branching processes
Nonuniform Berry-Esseen bounds
Random environment
Wasserstein-1 distance

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10.3770/j.issn:2095-2651.2023.06.009

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abstract = "Let (Zn)n≥0 be a supercritical branching process in an independent and identically distributed random environment. We establish an optimal convergence rate in the Wasserstein-1 distance for the process (Zn)n≥0, which completes a result of Grama et al. [Stochastic Process. Appl., 2017, 127(4): 1255–1281]. Moreover, an exponential nonuniform Berry-Esseen bound is also given. At last, some applications of the main results to the confidence interval estimation for the criticality parameter and the population size Zn are discussed.",

keywords = "Branching processes, Nonuniform Berry-Esseen bounds, Random environment, Wasserstein-1 distance",

author = "Hao Wu and Xiequan Fan and Zhiqiang Gao and Yinna Ye",

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AU - Wu, Hao

AU - Fan, Xiequan

AU - Gao, Zhiqiang

AU - Ye, Yinna

PY - 2023

Y1 - 2023

N2 - Let (Zn)n≥0 be a supercritical branching process in an independent and identically distributed random environment. We establish an optimal convergence rate in the Wasserstein-1 distance for the process (Zn)n≥0, which completes a result of Grama et al. [Stochastic Process. Appl., 2017, 127(4): 1255–1281]. Moreover, an exponential nonuniform Berry-Esseen bound is also given. At last, some applications of the main results to the confidence interval estimation for the criticality parameter and the population size Zn are discussed.

AB - Let (Zn)n≥0 be a supercritical branching process in an independent and identically distributed random environment. We establish an optimal convergence rate in the Wasserstein-1 distance for the process (Zn)n≥0, which completes a result of Grama et al. [Stochastic Process. Appl., 2017, 127(4): 1255–1281]. Moreover, an exponential nonuniform Berry-Esseen bound is also given. At last, some applications of the main results to the confidence interval estimation for the criticality parameter and the population size Zn are discussed.

KW - Branching processes

KW - Nonuniform Berry-Esseen bounds

KW - Random environment

KW - Wasserstein-1 distance

UR - https://www.scopus.com/pages/publications/105014257849

U2 - 10.3770/j.issn:2095-2651.2023.06.009

DO - 10.3770/j.issn:2095-2651.2023.06.009

M3 - Article

AN - SCOPUS:105014257849

SN - 2095-2651

VL - 43

SP - 737

EP - 753

JO - Journal of Mathematical Research with Applications

JF - Journal of Mathematical Research with Applications

IS - 6

ER -

Wasserstein-1 Distance and Nonuniform Berry-Esseen Bound for a Supercritical Branching Process in a Random Environment

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Keywords

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