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

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  • Komorowski, Tomasz
  • Walczuk, Anna

Abstract

Suppose that {Xt,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 ∫0Tψ(Xs)ds, provided that the dual transition probability semigroup, defined on measures, is strongly contractive in an appropriate Wasserstein metric. Function ψ is assumed to be Lipschitz on E.

Suggested Citation

  • Komorowski, Tomasz & Walczuk, Anna, 2012. "Central limit theorem for Markov processes with spectral gap in the Wasserstein metric," Stochastic Processes and their Applications, Elsevier, vol. 122(5), pages 2155-2184.
  • Handle: RePEc:eee:spapps:v:122:y:2012:i:5:p:2155-2184
    DOI: 10.1016/j.spa.2012.03.006
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    References listed on IDEAS

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    1. Holzmann, Hajo, 2005. "Martingale approximations for continuous-time and discrete-time stationary Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 115(9), pages 1518-1529, September.
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