On Sub-Geometric Ergodicity of Diffusion Processes

Abstract

In this article, we discuss ergodicity properties of a diffusion process given through an Itô stochastic differential equation. We identify conditions on the drift and diffusion coefficients which result in sub-geometric ergodicity of the corresponding semigroup with respect to the total variation distance. We also prove sub-geometric contractivity and ergodicity of the semigroup under a class of Wasserstein distances. Finally, we discuss sub-geometric ergodicity of two classes of Markov processes with jumps.

References in corpus (5)

• Subgeometric ergodicity of strong Markov processes
• Coupling for Ornstein--Uhlenbeck processes with jumps
• Coupling and exponential ergodicity for stochastic differential equations driven by Lévy processes
• $L^p$-Wasserstein distance for stochastic differential equations driven by Lévy processes
• Subgeometric rates of convergence for Markov processes under subordination