A note on the uniform ergodicity of diffusion processes

Nikola Sandrić

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arXiv · 2503.06111

A note on the uniform ergodicity of diffusion processes

Nikola Sandrić

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Abstract

In this note, we discuss the uniform ergodicity of a diffusion process given by an It\^o stochastic differential equation. We present an integral condition in terms of the drift and diffusion coefficients that ensures the uniform ergodicity of the corresponding transition kernel with respect to the total variation distance. Applications of the obtained results to a class of subordinate diffusion processes are also presented.

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Nikola Sandrić. 2025-03-08. A note on the uniform ergodicity of diffusion processes. https://arxiv.org/abs/2503.06111

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