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Wasserstein Convergence Rates for Empirical Measures of Subordinated Processes on Noncompact Manifolds

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  • Huaiqian Li

    (Tianjin University)

  • Bingyao Wu

    (Tianjin University)

Abstract

The asymptotic behavior of empirical measures has been studied extensively. In this paper, we consider empirical measures of given subordinated processes on complete (not necessarily compact) and connected Riemannian manifolds with possibly nonempty boundary. We obtain rates of convergence for empirical measures to the invariant measure of the subordinated process under the Wasserstein distance. The results, established for more general subordinated processes than ( arXiv:2107.11568 ), generalize the recent ones in Wang (Stoch Process Appl 144:271–287, 2022) and are shown to be sharp by a typical example. The proof is motivated by the aforementioned works.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jotpro:v:36:y:2023:i:2:d:10.1007_s10959-022-01196-8
    DOI: 10.1007/s10959-022-01196-8
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    References listed on IDEAS

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    1. 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.
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