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

Suppose that {X-l, t >= 0} is a non-stationary Markov process, taking values in a Polish metric space E. We prove the law of large numbers and central limit theorem for an additive functional of the form integral(T)(0) Psi (X-s)ds, provided that the dual transition probability semigroup, defined on measures, is strongly contractive in an appropriate Wasserstein metric. Function Psi is assumed to be Lipschitz on E. (C) 2012 Elsevier B.V. All rights reserved.