engleski

On Sub-Geometric Ergodicity of Diffusion Processes

In this article, we discuss ergodicity properties of a diffusion process given through an It\^{; ; ; ; o}; ; ; ; 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.

asymptotic flatness, diffusion process, sub-geometric ergodicity, total variation distance, Wasserstein distance

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