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

In this paper, we study the rate of convergence in total variation distance for time continuous Markov processes, by using some I ψ and I ψ , 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). [ABSTRACT FROM AUTHOR]