A central limit theorem for singularly perturbed nonstationary finite state Markov chains
Zhang, Q. ; Yin, G.
Ann. Appl. Probab., Tome 6 (1996) no. 1, p. 650-670 / Harvested from Project Euclid
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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.
Publié le : 1996-05-14
Classification:  Finite state Markov chain,  singular perturbation,  Gaussian process,  60F05,  60J27,  34E05,  93E20 
@article{1034968148,
     author = {Zhang, Q. and Yin, G.},
     title = {A central limit theorem for singularly perturbed nonstationary
		 finite state Markov chains},
     journal = {Ann. Appl. Probab.},
     volume = {6},
     number = {1},
     year = {1996},
     pages = { 650-670},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1034968148}
}

Zhang, Q.; Yin, G. A central limit theorem for singularly perturbed nonstationary
		 finite state Markov chains. Ann. Appl. Probab., Tome 6 (1996) no. 1, pp.  650-670. http://gdmltest.u-ga.fr/item/1034968148/