Positive multiplications in difference equations: With an appendix by David R. McDonald
type: Item
instance of: scholarly article
title: Positive multiplications in difference equations: With an appendix by David R. McDonald
zbMATH Open document ID: 0826.39001
author: Jeremy D. Gould
author: David Handelman
published in: Journal of Functional Analysis
publication date: 1995-12-03T00:00:00Z
review text: The authors study the generalizations of three-term recurrence relations with respect to positivity and what amounts to a boundary for the corresponding Markov chains. They show that an eventual ``linearization'' property holds. They also obtain limit ratio theorems for many of the random walks/Markov chains. The techniques used here are a mixture of algebra and functional analysis, with some ideas from the version of Choquet theory developed for dimension groups by \textit{E. G. Effros}, \textit{D. E. Handelman}, and \textit{C.-L. Shen} [Am. J. Math. 102, 385-407 (1980; Zbl 0457.46047)] and others. In the end of the paper there is an appendix by D. R. McDonald giving fairly general conditions under which stationary Markov chains on the positive integers have trivial Poisson boundary. This is used in the main part of the paper to treat a larger class of recurrence relations.
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 39A10
Mathematics Subject Classification ID: 60G50
zbMATH DE Number: 763975
zbMATH Keywords: linearization
zbMATH Keywords: three-term recurrence relations
zbMATH Keywords: positivity
zbMATH Keywords: Markov chains
zbMATH Keywords: limit ratio theorems
zbMATH Keywords: random walks
zbMATH Keywords: Choquet theory
zbMATH Keywords: dimension groups
zbMATH Keywords: Poisson boundary
MaRDI profile type: Publication
full work available at URL: jfan.1994.1152
OpenAlex ID: W2091677077
DOI: 10.1006/JFAN.1994.1152
description: scientific article; zbMATH DE number 763975