论文标题
瓦斯坦的收敛，用于riemannian歧管上属于dirichlet扩散的经验度量
Wasserstein Convergence for Empirical Measures of Subordinated Dirichlet Diffusions on Riemannian Manifolds
论文作者
论文摘要
我们研究了紧凑型riemannian歧管$ m $，在二次瓦斯特因距离下，在紧凑的riemannian歧管$ m $上，与边界$ \ partial m $相关的经验措施的长期行为。对于任何不集中在$ \ partial m $上的初始分布，我们获得了收敛速度，甚至获得了在退出$ m \ setMinus \ partial m $后杀死的过程中的二次二次瓦斯坦距离的有条件期望的确切限制。特别是，结果与F.-Y.最近证明的结果一致。 wang in \ cite {ew2}用于dirichlet扩散过程。
We investigate long-time behaviors of empirical measures associated with subordinated Dirichlet diffusion processes on a compact Riemannian manifold $M$ with boundary $\partial M$ to some reference measure, under the quadratic Wasserstein distance. For any initial distribution not concentrated on $\partial M$, we obtain the rate of convergence and even the precise limit for the conditional expectation of the quadratic Wasserstein distance conditioned on the process killed upon exiting $M\setminus\partial M$. In particular, the results coincide with the recent ones proved by F.-Y. Wang in \cite{eW2} for Dirichlet diffusion processes.
