From law of the iterated logarithm to Zolotarev distance for supercritical branching processes in random environment

Yinna Ye

doi:10.1016/j.spl.2024.110194

From law of the iterated logarithm to Zolotarev distance for supercritical branching processes in random environment

Yinna Ye

Department of Applied Mathematics

Xi'an Jiaotong-Liverpool University

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

Abstract

Consider (Z_n)_n⩾0 a supercritical branching process in an independent and identically distributed environment. Based on some recent development in martingale limit theory, we established law of the iterated logarithm, strong law of large numbers, invariance principle and optimal convergence rate in the central limit theorem under Zolotarev and Wasserstein distances of order p∈(0,2] for the process (logZ_n)_n⩾0.

Original language	English
Article number	110194
Number of pages	8
Journal	Statistics and Probability Letters
Volume	214
DOIs	https://doi.org/10.1016/j.spl.2024.110194
Publication status	Published - Nov 2024

Keywords

Branching processes in random environment
Convergence rates in central limit theorem
Law of large numbers
Law of the iterated logarithm
Wasserstein distance
Zolotarev distance

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10.1016/j.spl.2024.110194Licence: CC BY-NC-ND

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abstract = "Consider (Zn)n⩾0 a supercritical branching process in an independent and identically distributed environment. Based on some recent development in martingale limit theory, we established law of the iterated logarithm, strong law of large numbers, invariance principle and optimal convergence rate in the central limit theorem under Zolotarev and Wasserstein distances of order p∈(0,2] for the process (logZn)n⩾0.",

keywords = "Branching processes in random environment, Convergence rates in central limit theorem, Law of large numbers, Law of the iterated logarithm, Wasserstein distance, Zolotarev distance",

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AB - Consider (Zn)n⩾0 a supercritical branching process in an independent and identically distributed environment. Based on some recent development in martingale limit theory, we established law of the iterated logarithm, strong law of large numbers, invariance principle and optimal convergence rate in the central limit theorem under Zolotarev and Wasserstein distances of order p∈(0,2] for the process (logZn)n⩾0.

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KW - Convergence rates in central limit theorem

KW - Law of large numbers

KW - Law of the iterated logarithm

KW - Wasserstein distance

KW - Zolotarev distance

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JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

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ER -

From law of the iterated logarithm to Zolotarev distance for supercritical branching processes in random environment

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