On Sub-Geometric Ergodicity of Diffusion Processes

Petra Lazić; Nikola Sandrić

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arXiv · 2006.01567

On Sub-Geometric Ergodicity of Diffusion Processes

Petra Lazić·Nikola Sandrić

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Abstract

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.

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Petra Lazić, Nikola Sandrić. 2020-06-02. On Sub-Geometric Ergodicity of Diffusion Processes. https://arxiv.org/abs/2006.01567

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