Ratio limits and limiting conditional distributions for discrete-time birth-death processes
type: Item
instance of: scholarly article
title: Ratio limits and limiting conditional distributions for discrete-time birth-death processes
zbMATH Open document ID: 0821.60088
author: Pauline Schrijner
author: Erik A. van Doorn
published in: Journal of Mathematical Analysis and Applications
publication date: 1995-09-27T00:00:00Z
full work available at URL: ratio-limits-and-limiting-conditional-distributions-for-discretetime-birthdeath-processes(5f311c37-6f81-4392-99c9-641a6e764a4d).html
review text: The authors study discrete-time birth-death processes with an absorbing state by considering the corresponding random walk polynomials for the \(n\)-step transition probabilities. Conditions are given for existence of limits of ratios of \(n\)-step transition probabilities for \(n \to \infty\). The conditional state distribution at time \(n\), given that absorption has not occurred by that time but will occur eventually, is studied. Conditions are given in which these distributions converge to a proper distribution. Finally, random walks related to Jacobi polynomials and random walks with almost constant parameters are studied.
Mathematics Subject Classification ID: 60J80
Mathematics Subject Classification ID: 60G50
zbMATH DE Number: 765123
zbMATH Keywords: birth-death processes
zbMATH Keywords: random walk
zbMATH Keywords: random walk polynomials
reviewed by: Annette Kopp-Schneider
MaRDI profile type: Publication
OpenAlex ID: W2103021283
Wikidata QID: Q105583266
DOI: 10.1006/JMAA.1995.1076
description: scientific article; zbMATH DE number 765123