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Convergence in Wasserstein distance for empirical measures of non-symmetric subordinated diffusion processes

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  • Wang, Feng-Yu

Abstract

By using the spectrum of the underlying symmetric diffusion operator, the convergence in Lp-Wasserstein distance Wp(p≥1) is characterized for the empirical measure μt of non-symmetric subordinated diffusion processes in an abstract framework. In particular, The precise acceleration in W2 is derived for divergence-free perturbations of symmetric diffusion processes. The main results are applied to the subordinations of several typical models, which include the (reflecting) diffusion processes on compact manifolds, the conditional diffusion processes, the Wright-Fisher diffusion process, and hypoelliptic diffusion processes on SU(2).

Suggested Citation

  • Wang, Feng-Yu, 2026. "Convergence in Wasserstein distance for empirical measures of non-symmetric subordinated diffusion processes," Stochastic Processes and their Applications, Elsevier, vol. 198(C).
    • Handle: RePEc:eee:spapps:v:198:y:2026:i:c:s0304414926001018
    DOI: 10.1016/j.spa.2026.104969
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    References listed on IDEAS

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    1. Wang, Feng-Yu & Wu, Bingyao & Zhu, Jie-Xiang, 2026. "Sharp Lq-convergence rate in p-Wasserstein distance for empirical measures of diffusion processes," Stochastic Processes and their Applications, Elsevier, vol. 195(C).
    2. Huesmann, Martin & Mattesini, Francesco & Trevisan, Dario, 2023. "Wasserstein asymptotics for the empirical measure of fractional Brownian motion on a flat torus," Stochastic Processes and their Applications, Elsevier, vol. 155(C), pages 1-26.
    3. Wang, Feng-Yu, 2022. "Wasserstein convergence rate for empirical measures on noncompact manifolds," Stochastic Processes and their Applications, Elsevier, vol. 144(C), pages 271-287.
    4. Mariani, Mauro & Trevisan, Dario, 2025. "Wasserstein asymptotics for Brownian motion on the flat torus and Brownian interlacements," Stochastic Processes and their Applications, Elsevier, vol. 183(C).
    5. Wang, Feng-Yu, 2005. "Gradient estimates and the first Neumann eigenvalue on manifolds with boundary," Stochastic Processes and their Applications, Elsevier, vol. 115(9), pages 1475-1486, September.
    6. Huaiqian Li & Bingyao Wu, 2023. "Wasserstein Convergence Rates for Empirical Measures of Subordinated Processes on Noncompact Manifolds," Journal of Theoretical Probability, Springer, vol. 36(2), pages 1243-1268, June.
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    1. Wang, Feng-Yu & Wu, Bingyao & Zhu, Jie-Xiang, 2026. "Sharp Lq-convergence rate in p-Wasserstein distance for empirical measures of diffusion processes," Stochastic Processes and their Applications, Elsevier, vol. 195(C).
    2. Mariani, Mauro & Trevisan, Dario, 2025. "Wasserstein asymptotics for Brownian motion on the flat torus and Brownian interlacements," Stochastic Processes and their Applications, Elsevier, vol. 183(C).
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    5. Huesmann, Martin & Mattesini, Francesco & Trevisan, Dario, 2023. "Wasserstein asymptotics for the empirical measure of fractional Brownian motion on a flat torus," Stochastic Processes and their Applications, Elsevier, vol. 155(C), pages 1-26.

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