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

Abstract

Suppose that $\{X_t,t\ge 0\}$ 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 ${\int }_0^T\psi (X_s)ds$, 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 $E$.

References in corpus (1)

• Spectral gaps in Wasserstein distances and the 2D stochastic Navier--Stokes equations

Cited by in corpus (4)

• Exponential rate of convergence for some Markov operators
• Transportation inequalities for non-globally dissipative SDEs with jumps via Malliavin calculus and coupling
• A central limit theorem for continuous-time Markov processes conditioned not to be absorbed
• An invariance principle for the law of the iterated logarithm for some Markov chains