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May 1996 A central limit theorem for singularly perturbed nonstationary finite state Markov chains
Q. Zhang, G. Yin
Ann. Appl. Probab. 6(2): 650-670 (May 1996). DOI: 10.1214/aoap/1034968148

Abstract

This work is concerned with the asymptotic properties of a singular perturbed nonstationary finite state Markov chain. In a recent paper of the authors, it was shown that as the fluctuation rate of the Markov chain goes to $\infty$, the probability distribution of the Markov chain converges to its time-dependent quasi-equilibrium distribution. In addition, asymptotic expansion of the probability distribution was obtained. This paper is a continuation of our effort in this direction. Upon using the asymptotic expansion, a suitably scaled sequence is examined in detail. Asymptotic normality is obtained. It is shown that the accumulated difference between the indicator process and the quasi-equilibrium distribution converges to a Gaussian process with zero mean. An explicit formula for the covariance function of the Gaussian process is obtained, which depends crucially on the asymptotic expansion.

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Q. Zhang. G. Yin. "A central limit theorem for singularly perturbed nonstationary finite state Markov chains." Ann. Appl. Probab. 6 (2) 650 - 670, May 1996. https://doi.org/10.1214/aoap/1034968148

Information

Published: May 1996
First available in Project Euclid: 18 October 2002

zbMATH: 0855.60018
MathSciNet: MR1398062
Digital Object Identifier: 10.1214/aoap/1034968148

Subjects:
Primary: 34E05 , 60F05 , 60J27 , 93E20

Keywords: Finite state Markov chain , Gaussian process , Singular perturbation

Rights: Copyright © 1996 Institute of Mathematical Statistics

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Vol.6 • No. 2 • May 1996
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