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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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    Cited by:

    1. Bao, Jianhai & Wang, Jian, 2022. "Coupling approach for exponential ergodicity of stochastic Hamiltonian systems with Lévy noises," Stochastic Processes and their Applications, Elsevier, vol. 146(C), pages 114-142.
    2. Uehara, Yuma, 2019. "Statistical inference for misspecified ergodic Lévy driven stochastic differential equation models," Stochastic Processes and their Applications, Elsevier, vol. 129(10), pages 4051-4081.
    3. Chen, Chuchu & Dang, Tonghe & Hong, Jialin & Zhou, Tau, 2023. "CLT for approximating ergodic limit of SPDEs via a full discretization," Stochastic Processes and their Applications, Elsevier, vol. 157(C), pages 1-41.
    4. Bryant Davis & James P. Hobert, 2021. "On the Convergence Complexity of Gibbs Samplers for a Family of Simple Bayesian Random Effects Models," Methodology and Computing in Applied Probability, Springer, vol. 23(4), pages 1323-1351, December.
    5. Majka, Mateusz B., 2017. "Coupling and exponential ergodicity for stochastic differential equations driven by Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 127(12), pages 4083-4125.
    6. Wang, Ya & Wu, Fuke & Yin, George, 2024. "Limit theorems of additive functionals for regime-switching diffusions with infinite delay," Stochastic Processes and their Applications, Elsevier, vol. 167(C).

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