Occupation measures of singularly perturbed Markov chains with absorbing states
type: Item
instance of: scholarly article
title: Occupation measures of singularly perturbed Markov chains with absorbing states
zbMATH Open document ID: 0958.60073
author: G. Badowski
author: G. Yin
author: Q. Zhang
publication date: 2001-03-28T00:00:00Z
review text: The authors continue their study of the asymptotic properties of occupation measures for singularly perturbed Markov chains with inclusion of absorbing states which has applications in production planning, queueing networks and system reliability [see \textit{G. G. Yin} and \textit{Q. Zhang}, Continuous-time Markov chains and applications: A singular perturbation approach (1998; Zbl 0896.60039)]. They separate the states in accordance with their rates of changes, regroup them with like or similar transition rates, and introduce a small parameter \(\varepsilon >0\) resulting in a singularly perturbed system. Such an approach leads to insights of the probabilistic structure of the underlying system, which are important to the further study and design of control policies for operating these systems. They study unscaled occupation measures, and derive a mean-square estimate on a sequence of occupation measures centered around their limit distribution and obtain the convergence of the aggregate process. Although the aggregated process itself may be non-Markovian, its weak limit is a Markov chain with much smaller state space. Moreover, a suitably scaled sequence consisting of a component of scaled occupation measures and a component of the aggregated process is shown to converge to a pair of processes with a switching diffusion component.
reviewed by: P. R. Parthasarathy
Mathematics Subject Classification ID: 60J27
zbMATH DE Number: 1471204
zbMATH Keywords: singularly perturbed Markov chain
zbMATH Keywords: absorbing state
MaRDI profile type: Publication
full work available at URL: s101149900025
OpenAlex ID: W2082399356
cites work: Q4861696
cites work: A singular perturbation approach to modeling and control of Markov chains
cites work: Q4265503
cites work: Aggregation of Variables in Dynamic Systems
cites work: Asymptotic Expansions of Singularly Perturbed Systems Involving Rapidly Fluctuating Markov Chains
cites work: Constructing asymptotic series for probability distributions of Markov chains with weak and strong interactions
cites work: Q4375487
cites work: A central limit theorem for singularly perturbed nonstationary finite state Markov chains
cites work: Structural properties of Markov chains with weak and strong interactions
cites work: Asymptotic properties of a singularly perturbed Markov chain with inclusion of transient states.
cites work: Singularly perturbed Markov chains: Convergence and aggregation
cites work: On Stochastic Processes Defined by Differential Equations with a Small Parameter
cites work: Q4693053
cites work: Q3344923
cites work: Weak convergence methods and singularly perturbed stochastic control and filtering problems
cites work: Q3136505
cites work: Q3721531
cites work: Optimal control of Markov chains admitting strong and weak interactions
cites work: Q3917278
DOI: 10.1007/S101149900025
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published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 1471204