Central limit theorem for Markov processes with spectral gap in the Wasserstein metric

Suppose that {Xt,t≥0}{Xt,t≥0} is a non-stationary Markov process, taking values in a Polish metric space EE. We prove the law of large numbers and central limit theorem for an additive functional of the form ∫0Tψ(Xs)ds, provided that the dual transition probability semigroup, defined on measures, is strongly contractive in an appropriate Wasserstein metric. Function ψψ is assumed to be Lipschitz on EE.