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May 2000 Asymptotic properties of a singularly perturbed Markov chain with inclusion of transient states
G. Badowski, G. Yin, Q. Zhang
Ann. Appl. Probab. 10(2): 549-572 (May 2000). DOI: 10.1214/aoap/1019487355

Abstract

This work is concerned with aggregations in a singularly perturbed Markov chain having a finite state space and fast and slow motions.The state space of the underlying Markov chain can be decomposed into several groups of recurrent states and a group of transient states.The asymptotic properties are studied through sequences of unscaled and scaled occupation measures.By treating the states within each recurrent class as a single state, an aggregated process is defined and shown to be convergent to a limit Markov chain.In addition, it is shown that a sequence of suitably rescaled occupation measures converges to a switching diffusion process weakly.

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G. Badowski. G. Yin. Q. Zhang. "Asymptotic properties of a singularly perturbed Markov chain with inclusion of transient states." Ann. Appl. Probab. 10 (2) 549 - 572, May 2000. https://doi.org/10.1214/aoap/1019487355

Information

Published: May 2000
First available in Project Euclid: 22 April 2002

zbMATH: 1054.60078
MathSciNet: MR1768223
Digital Object Identifier: 10.1214/aoap/1019487355

Subjects:
Primary: 34E05 , 60B10 , 60F17 , 60J27

Keywords: Aggregation , occupation measure , singularly perturbed Markov chain , switching diffusion. , weak convergence

Rights: Copyright © 2000 Institute of Mathematical Statistics

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Vol.10 • No. 2 • May 2000
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