Estimating the stationary distribution of a Markov chain |
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| Authors: | Krishna B Athreya Mukul Majumdar |
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| Institution: | (1) Department of Operations Research and Industrial Engineering, Rhodes Hall, Cornell University, Ithaca, NY 14853, USA (e-mail: athreya@orie.cornell.edu) , US;(2) Department of Economics, Uris Hall, Cornell University, Ithaca, NY 14853, USA (e-mail: mkm5@cornell.edu) , US |
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| Abstract: | Summary. Let be a Markov chain with a unique stationary distribution . Let h be a bounded measurable function. Write and . This paper explores conditions for the consistency and asymptotic normality of the estimate of of assuming the existence of a solution to the Poisson equation . Our framework covers the case of nonirreducible Markov chains arising in many growth models in economics.
Received: October 8, 2001; revised version: April 8, 2002
RID="*"
ID="*" Thanks are due to Professors Rabi Bhattacharya, Nicholas Kiefer and Timothy Vogelsang on an earlier draft for helpful
conversations, and a referee for insightful comments.
Correspondence to: M.Majumdar |
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| Keywords: | and Phrases: Markov chains Stationary distribution Consistency Asymptotic normality Poisson equation Martingale central limit theorem |
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