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

Loïc Hervé and James Ledoux

Statistics & Probability Letters, 2021, vol. 179, issue C

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.

Keywords: Non-homogeneous Markov chains; Doeblin’s coefficient (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spl.2021.109204

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