TY - JOUR
T1 - Wasserstein-1 Distance and Nonuniform Berry-Esseen Bound for a Supercritical Branching Process in a Random Environment
AU - Wu, Hao
AU - Fan, Xiequan
AU - Gao, Zhiqiang
AU - Ye, Yinna
N1 - Publisher Copyright:
© 2023, Dalian University of Technology. All rights reserved.
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 -