Branching processes with negative offspring distributions
type: Item
instance of: scholarly article
title: Branching processes with negative offspring distributions
zbMATH Open document ID: 1025.60036
author: Ioana Dumitriu
author: Catherine Yan
author: Joel Spencer
published in: Annals of Combinatorics
publication date: 2003-08-14T00:00:00Z
review text: Let \(Z_n\), \(n=0,1,2,\dots\), be i.i.d. random variables, define \(Y_0:=1\), \(Y_i:= Y_{i-1}+ 1-Z_i\), \(i=1,2, \dots\), and let \(T\) be the minimal \(i\) for which \(Z\leq 0\), with \(T=\infty\) if no such \(i\) exists. The escape probability \(P(T= \infty)\) is computed first purely probabilistically and then again analytically, employing a method that has already been used successfully with branching processes. It also leads to the asymptotics of \(P(T>N)\) and \(P(T=\infty \mid T>N)\).
Mathematics Subject Classification ID: 60J80
Mathematics Subject Classification ID: 60K25
zbMATH DE Number: 1964623
zbMATH Keywords: branching process
zbMATH Keywords: negative offspring
zbMATH Keywords: single server queue
reviewed by: Heinrich Hering
MaRDI profile type: Publication
full work available at URL: s000260300003
OpenAlex ID: W2018030835
DOI: 10.1007/S000260300003
description: scientific article; zbMATH DE number 1964623