Convergence in total variation distance for (in)homogeneous Markov processes

Yong-Hua Mao, Liping Xu, Ming Zhang and Yu-Hui Zhang

Statistics & Probability Letters, 2018, vol. 137, issue C, 54-62

Abstract: In this paper, we study the rate of convergence in total variation distance for time continuous Markov processes, by using some Iψ and Iψ,t-inequalities. For homogeneous reversible process, we use some homogeneous inequalities, including the Poincaré and relative entropy inequalities. For the time-inhomogeneous diffusion process, we use some inhomogeneous inequalities, including the time-dependent Poincaré and Log-Sobolev inequalities. This extends some results for the time-homogeneous diffusion processes in Cattiaux and Guillin (2009).

Keywords: (In)homogeneous Markov processes; Functional inequalities; Rate of convergence; Total variation distance (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1016/j.spl.2018.01.011

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