Existence, uniqueness, and constructions for stochastically monotone \(Q\)-processes
type: Item
instance of: scholarly article
title: Existence, uniqueness, and constructions for stochastically monotone \(Q\)-processes
zbMATH Open document ID: 0946.60075
author: Anyue Chen
author: Hanjun Zhang
published in: Southeast Asian Bulletin of Mathematics
publication date: 2000-02-23T00:00:00Z
review text: A (standard) transition function \(P(t)=\{P_{ij} (t):i,j \in E\}\) for a continuous-time Markov chain on \(E=\{0,1, \dots\}\) is said to be stochastically monotone if \(\sum^\infty_{j=k} P_{ij}(t)\) is a non-decreasing function of \(i\) for each fixed \(k\in E\) and \(t\geq 0\). The author addresses the questions of existence and uniqueness of stochastically monotone \(Q\)-functions for a given conservative \(q\)-matrix \(Q\). He shows that there is at most one stochastically monotone \(Q\)-function and gives conditions under which such a \(Q\)-function (i) exists and (ii) equals the minimal \(Q\)-function. Also, it is shown how the stochastically monotone \(Q\)-function can be constructed if it is not the minimal \(Q\)-function.
Mathematics Subject Classification ID: 60J27
Mathematics Subject Classification ID: 60J35
zbMATH DE Number: 1406290
zbMATH Keywords: stochastic monotonicity
zbMATH Keywords: duality
reviewed by: Erik A. van Doorn
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1406290