Estimating the stationary distribution of a Markov chain

Abstract

Let {X_j}^∞₀ be a Markov chain with a unique stationary distribution π . Let h be a bounded measurable function. Write λ _h=hdπ and λ_hn=1/(n+1) ⁿ₀h(X_j). This paper explores conditions for the consistency and asymptotic normality of the estimate of λ_hn of λ _h assuming the existence of a solution to the Poisson equation h-λ _h=g-P_g. Our framework covers the case of nonirreducible Markov chains arising in many growth models in economics.