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

Loïc Hervé (1) , James Ledoux (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

The asymptotic of products of general Markov/transition kernels is investigated using Doeblin's coefficient. We propose a very 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 explicitly dened from the two parameters in the minorization condition associated with the Doeblin coefficient. This allows us to extend various standard convergence results to general Markov chains and to propose a new result on forward/backward products of random Markov kernels.

Mots clés: 60B20 Keywords : Non-homogeneous Markov chains; Doeblin's coefficient; AMS subject classication : 60J05; 60F99

Domaines: Probabilités [math.PR]

Loïc Hervé, James Ledoux. Asymptotic of products of Markov kernels. Application to deterministic and random forward/backward products. 2019. ⟨hal-02354594v1⟩