论文标题
Wasserstein收敛速率用于非伴动歧管上次级过程的经验度量
Wasserstein Convergence Rates for Empirical Measures of Subordinated Processes on Noncompact Manifolds
论文作者
论文摘要
经验措施的渐近行为已被广泛研究。在本文中，我们考虑了完整（不一定是紧凑）和连接的Riemannian流形的经验度量，并可能具有非空边界。我们获得了经验措施的收敛速率，以达到瓦斯坦斯坦距离下次级过程的不变度度量。该结果是针对比[Arxiv：2107.11568]更一般的次级过程建立的，它在[Stoch中概括了最近的过程。 Proc。应用。 144（2022），271--287]，通过一个典型的例子被证明是锋利的。证据是由上述作品激励的。
The asymptotic behaviour 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 [Stoch. Proc. Appl. 144(2022), 271--287] and are shown to be sharp by a typical example. The proof is motivated by the aforementioned works.
