Ergodicity of Spitzer's renewal model
type: Item
instance of: scholarly article
title: Ergodicity of Spitzer's renewal model
zbMATH Open document ID: 0818.60076
DOI: 10.1016/0304-4149(94)00029-S
author: Vladas Sidoravicius
author: Maria Eulalia Vares
published in: Stochastic Processes and their Applications
publication date: 1995-08-17T00:00:00Z
review text: Assume at each point \(x\) of the \(d\)-dimensional integer lattice sits some renewing object with age \(\eta (x)\). It undergoes death and immediate renewal with renewal rate equal to the average age of its closest neighbors plus a constant \(c\). A stochastic process modelling this situation is defined and analysed. It generalizes the process defined by \textit{E. D. Andjel} and \textit{M. E. Vares} [ibid. 42, No. 2, 215-236 (1992; Zbl 0757.60085)] in the case \(d = 1\). The main result states that the process is ergodic if and only if \(c > 0\).
Mathematics Subject Classification ID: 60K05
zbMATH DE Number: 735476
zbMATH Keywords: attractiveness
zbMATH Keywords: absence of phase transition
zbMATH Keywords: Gibbs measure
zbMATH Keywords: renewal rate
reviewed by: Helmut Wegmann
MaRDI profile type: Publication
cites work: Ergodicity of an infinite dimensional renewal process
cites work: Q5711199
cites work: Gibbs measures and phase transitions
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full work available at URL: 0304-4149(94)00029-s
OpenAlex ID: W1986956475
description: scientific article; zbMATH DE number 735476