论文标题
Wasserstein收敛，用于在Riemannian歧管上的下属Dirichlet扩散的条件经验度量
Wasserstein Convergence for Conditional Empirical Measures of Subordinated Dirichlet Diffusions on Riemannian Manifolds
论文作者
论文摘要
经验措施的渐近行为有很多研究。但是，对条件经验措施的研究是有限的。在王\ cite {ew1}的发展下，在二次瓦斯汀距离下，我们研究了与属于dirichlet扩散过程相关的条件经验措施的收敛速率，这些量子与吸收边界相关的紧凑型riemannian歧管上。我们给出任何初始分布的收敛速度，并证明了大型初始分布的精确限制。我们遵循王的基本思想，但要使自己在证据中造成重大偏差，以克服我们的非本地环境中的困难。
The asymptotic behaviour of empirical measures has plenty of studies. However, the research on conditional empirical measures is limited. Being the development of Wang \cite{eW1}, under the quadratic Wasserstein distance, we investigate the rate of convergence of conditional empirical measures associated to subordinated Dirichlet diffusion processes on a connected compact Riemannian manifold with absorbing boundary. We give the sharp rate of convergence for any initial distribution and prove the precise limit for a large class of initial distributions. We follow the basic idea of Wang, but allow ourselves substantial deviations in the proof to overcome difficulties in our non-local setting.
