Strongly monotone \(q\)-functions and a note on strong ergodicity of monotone \(q\)-functions
type: Item
instance of: scholarly article
title: Strongly monotone \(q\)-functions and a note on strong ergodicity of monotone \(q\)-functions
zbMATH Open document ID: 1119.60062
published in: Statistics \& Probability Letters
publication date: 2007-04-19T00:00:00Z
review text: A transition function \( P\left( t\right) =(p_{ij}\left( t\right) )_{i,j\in \mathbb{N}},t\geq 0\), is said to be strongly monotone if \(\sum_{k\geq j}p_{ik}\left( t\right) \) and \( p_{ij}\left( t\right) \rightarrow 0\) as \(i\rightarrow \infty \) for any \(j\in \mathbb{N}\) and \(t\geq 0\). For a stable \(q\)-matrix \(Q\), the author gives a necessary and sufficient condition for the minimal \(Q\)-function \(P\left( t\right) \) to be strongly monotone. This yields a criterion for a Feller minimal monotone chain to be strongly ergodic. Finally, an application to birth-and-death processes with killing is given.
Mathematics Subject Classification ID: 60J27
Mathematics Subject Classification ID: 60J80
zbMATH DE Number: 5144924
zbMATH Keywords: monotone transition function
zbMATH Keywords: Feller-Reuter-Riley transition function
zbMATH Keywords: \(q\)-matrix
zbMATH Keywords: birth-and-death process
zbMATH Keywords: ergodicity
author: Yangrong Li
reviewed by: Marius Iosifescu
MaRDI profile type: Publication
full work available at URL: j.spl.2006.08.005
OpenAlex ID: W2018450693
cites work: Some remarks on the duality of continuous time markov chains
cites work: Applications of Feller-Reuter-Riley transition functions
cites work: Existence, uniqueness, and constructions for stochastically monotone \(Q\)-processes
cites work: Extinction Probability in A Birth-Death Process with Killing
cites work: Q4119915
cites work: Contraction integrated semigroups and their application to continuous-time Markov chains
cites work: Dual and Feller-Reuter-Riley transition functions
cites work: The Feller Property for Markov Semigroups on a Countable State Space
cites work: The equivalence of absorbing and reflecting barrier problems for stochastically monotone Markov processes
cites work: Stochastic comparability and dual \(Q\)-functions
cites work: Strong ergodicity of monotone transition functions
DOI: 10.1016/J.SPL.2006.08.005
description: scientific article; zbMATH DE number 5144924