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<p>The convergence rate in Wasserstein distance is estimated for empirical measures of ergodic Markov processes, and the estimate can be sharp in some specific situations. The main result is applied to subordinations of typical models excluded by existing results, which include: stochastic Hamiltonian systems on <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="245_2025_10275_Article_IEq1.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="62" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathbb{R}}^{n}\times {\mathbb{R}}^{m}\)</EquationSource> </InlineEquation>, spherical velocity Langevin processes on <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="245_2025_10275_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="78" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathbb{R}}^n\times \mathbb S^{n-1},\)</EquationSource> </InlineEquation> multi-dimensional Wright–Fisher type diffusion processes, and stable type jump processes.</p>

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Wasserstein Convergence Rate for Empirical Measures of Markov Processes

  • 期刊论文

  • 发表日期：

    2025年6月24日

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  • Feng-Yu Wang

摘要

The convergence rate in Wasserstein distance is estimated for empirical measures of ergodic Markov processes, and the estimate can be sharp in some specific situations. The main result is applied to subordinations of typical models excluded by existing results, which include: stochastic Hamiltonian systems on \({\mathbb{R}}^{n}\times {\mathbb{R}}^{m}\) , spherical velocity Langevin processes on \({\mathbb{R}}^n\times \mathbb S^{n-1},\) multi-dimensional Wright–Fisher type diffusion processes, and stable type jump processes.