A continuous-time Markov chain under the influence of a regulating point process and applications in stochastic models with catastrophes
type: Item
instance of: scholarly article
title: A continuous-time Markov chain under the influence of a regulating point process and applications in stochastic models with catastrophes
zbMATH Open document ID: 1030.60069
DOI: 10.1016/S0377-2217(02)00465-4
author: Antonis Economou
author: Demetrios Fakinos
published in: European Journal of Operational Research
publication date: 2003-07-30T00:00:00Z
review text: A continuous time Markov process with discrete state space \(S\) is modified by introducing additional jumps. They occur at time instants \(t_i\) and result in state \(A(t_i)\), \(i=1,2,\dots\), where \(A : [0,\infty)\to S\) is a given piecewise constant function. The time instants \(t_i\) may be random, i.e. be given by a point process \(X\) on \([0,\infty)\). It seems that the authors presume that the sequence has a.s. no finite accumulation points. They discuss several special cases, where the transition probabilities of the modified process can be determined more or less explicitly, for instance the case where \(X\) is a renewal process with special life time distributions, the case where the original Markov process is time homogeneous, is a birth-death process, or is the queueing process in a Markovian setup. Numerical results on the transient behavior of the modified process in some special examples are added.
reviewed by: Helmut Wegmann
Mathematics Subject Classification ID: 60J27
Mathematics Subject Classification ID: 60K25
zbMATH DE Number: 1957063
zbMATH Keywords: stochastic processes
zbMATH Keywords: continuous time Markov chain
zbMATH Keywords: regulating point process
zbMATH Keywords: renewal process
zbMATH Keywords: transient distribution
zbMATH Keywords: stationary distribution
zbMATH Keywords: catastrophes
zbMATH Keywords: queueing process
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1957063