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Asymptotic of products of Markov kernels. Application to deterministic and random forward/backward products

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  • Hervé, Loïc
  • Ledoux, James

Abstract

The asymptotic of products of general Markov/transition kernels is investigated using Doeblin’s coefficient. We propose a general approximating scheme as well as a convergence rate in total variation of such products by a sequence of positive measures. These approximating measures and the control of convergence are explicit from the two parameters in the minorization condition associated with the Doeblin coefficient. This allows us to extend the well-known forward/backward convergence results for stochastic matrices to general Markov kernels. A new result for forward/backward products of random Markov kernels is also established.

Suggested Citation

  • Hervé, Loïc & Ledoux, James, 2021. "Asymptotic of products of Markov kernels. Application to deterministic and random forward/backward products," Statistics & Probability Letters, Elsevier, vol. 179(C).
    • Handle: RePEc:eee:stapro:v:179:y:2021:i:c:s0167715221001668
    DOI: 10.1016/j.spl.2021.109204
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    References listed on IDEAS

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    1. Coppersmith, Don & Wu, Chai Wah, 2008. "Conditions for weak ergodicity of inhomogeneous Markov chains," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 3082-3085, December.
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    Cited by:

    1. Truquet, Lionel, 2023. "Strong mixing properties of discrete-valued time series with exogenous covariates," Stochastic Processes and their Applications, Elsevier, vol. 160(C), pages 294-317.

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