Complete left tail asymptotic for the density of branching processes in the Schröder case
type: Item
instance of: scholarly article
title: Complete left tail asymptotic for the density of branching processes in the Schröder case
zbMATH Open document ID: 1548.60125
author: Anton A. Kutsenko
published in: The Journal of Fourier Analysis and Applications
publication date: 2024-07-17T00:00:00Z
review text: Consider a Galton-Watson process with offspring distribution satisfying \(p_0=0\) and \(p_1\in (0, 1)\). Assume that the mean number of offspring is finite.The author uses Fourier analysis method to study the density \(p(x)\) of the limit of the fundamental martingale and establishes a complete expansion of \(p(x)\). This sharpens the result obtained by \textit{J. D. Biggins} and \textit{N. H. Bingham} [Adv. Appl. Probab. 25, No. 4, 757--772 (1993; Zbl 0796.60090)].
reviewed by: Renming Song
Mathematics Subject Classification ID: 60J80
zbMATH DE Number: 7882013
zbMATH Keywords: Galton-Watson process
zbMATH Keywords: left tail asymptotic
zbMATH Keywords: Schröder and Poincaré-type functional equations
zbMATH Keywords: Karlin-McGregor function
zbMATH Keywords: Fourier analysis
MaRDI profile type: Publication
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DOI: 10.1007/S00041-024-10096-W
description: scientific article; zbMATH DE number 7882013