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

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

2011-02-09

arxiv.org/abs/1102.1842v6

Mathematics

Probability

Scientific paper

Suppose that $\{X_t,\,t\ge0\}$ 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 $E$.

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