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<p>In this note, we discuss the uniform ergodicity of a diffusion process given by an Itô 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.</p>

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A Note on the Uniform Ergodicity of Diffusion Processes

  • 期刊论文

  • 发表日期：

    2025年3月13日

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  • Nikola Sandrić

摘要

In this note, we discuss the uniform ergodicity of a diffusion process given by an Itô 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.