From law of the iterated logarithm to Zolotarev distance for supercritical branching processes in random environment
type: Item
instance of: scholarly article
title: From law of the iterated logarithm to Zolotarev distance for supercritical branching processes in random environment
zbMATH Open document ID: 1547.6008
author: Yinna Ye
published in: Statistics \& Probability Letters
publication date: 2024-09-16T00:00:00Z
review text: The author considers a supercritical branching process in a random environment \((Z_n)_{n\geq0}\) given by \(Z_0=1\) and \(Z_{n+1}=\sum_{i=1}^nX_{n,i}\) for \(n\geq0\), where there exist IID random variables \(\xi_0,\xi_1,\ldots\) such that, conditional on \(\xi_n\), we have that \((X_{n,i})_{i\geq1}\) is a sequence of IID random variables; these latter random variables also independent of \(Z_1,\ldots,Z_n\). Within this framework, the author uses martingale limit theory to establish limiting properties of \((\log Z_n)_{n\geq0}\), including a law of the iterated logarithm, a strong law of large numbers, an invariance principle, and central limit theorems with explicit rates of convergence to a Gaussian limit in the Zolotarev and Wasserstein distances of order \(p\in(0,2]\).
reviewed by: Fraser Daly
Mathematics Subject Classification ID: 60J80
Mathematics Subject Classification ID: 60K37
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 62E20
zbMATH DE Number: 7913923
zbMATH Keywords: branching processes in random environment
zbMATH Keywords: law of the iterated logarithm
zbMATH Keywords: law of large numbers
zbMATH Keywords: convergence rates in central limit theorem
zbMATH Keywords: Zolotarev distance
zbMATH Keywords: Wasserstein distance
MaRDI profile type: Publication
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DOI: 10.1016/J.SPL.2024.110194
description: scientific article; zbMATH DE number 7913923