In this paper we consider Foster–Liapounov-type drift conditions for Markov chains which imply polynomial rate convergence to stationarity in appropriate V-norms. We also show how these results can be used to prove central limit theorems for functions of the Markov chain. We consider two examples concerning random walks on the half line and the independence sampler.
"Polynomial Convergence Rates of Markov Chains." Ann. Appl. Probab. 12 (1) 224 - 247, February 2002. https://doi.org/10.1214/aoap/1015961162