Solving the Poisson equation using coupled Markov chains
本文展示如何利用耦合马尔可夫链生成泊松方程解的无偏估计量，并构造马尔可夫链遍历均值的渐近方差的无偏估计，为统计计算提供新方法。
This article shows how coupled Markov chains that meet exactly after a random number of iterations can be used to generate unbiased estimators of the solutions of the Poisson equation. Through this connection, we rederive known unbiased estimators of expectations with respect to the stationary distribution of a Markov chain and provide conditions for the finiteness of their moments. We further construct unbiased estimators of the asymptotic variance of Markov chain ergodic averages, and provide conditions for the finiteness of the estimators’ moments of any order. If their second moment is finite, the average of independent copies of such estimators converges to the asymptotic variance at the Monte Carlo rate, comparing favorably to known rates for batch means and spectral variance estimators. The results are illustrated with numerical experiments.