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

Huaiqian Li () and Bingyao Wu ()
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Huaiqian Li: Tianjin University
Bingyao Wu: Tianjin University

Journal of Theoretical Probability, 2023, vol. 36, issue 2, 1243-1268

Abstract: 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.

Keywords: Empirical measure; Subordinated process; Wasserstein distance; Heat flow; Riemannian manifold; Primary 60D05; 58J65; Secondary 60J60; 60J76 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10959-022-01196-8

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