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On asymptotics for Vaserstein coupling of Markov chains

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  • Butkovsky, O.A.
  • Veretennikov, A.Yu.

Abstract

We prove that strong ergodicity of a Markov process is linked with a spectral radius of a certain “associated” semigroup operator, although, not a “natural” one. We also give sufficient conditions for weak ergodicity and provide explicit estimates of the convergence rate. To establish these results we construct a modification of the Vaserstein coupling. Some applications including mixing properties are also discussed.

Suggested Citation

  • Butkovsky, O.A. & Veretennikov, A.Yu., 2013. "On asymptotics for Vaserstein coupling of Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 123(9), pages 3518-3541.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:9:p:3518-3541
    DOI: 10.1016/j.spa.2013.04.016
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    References listed on IDEAS

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    1. Yuri Kabanov & Robert Liptser, 2006. "From Stochastic Calculus to Mathematical Finance. The Shiryaev Festschrift," Post-Print hal-00488295, HAL.
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    Cited by:

    1. Alain Durmus & Eric Moulines & Alexey Naumov & Sergey Samsonov, 2024. "Probability and Moment Inequalities for Additive Functionals of Geometrically Ergodic Markov Chains," Journal of Theoretical Probability, Springer, vol. 37(3), pages 2184-2233, September.

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