论文标题
通过斯坦因的方法近似Riemannian措施
Approximation of Riemannian measures by Stein's method
论文作者
论文摘要
在本文中，我们介绍了一种理论上的基础，以对斯坦因歧管上的概率分布的方法进行方法。使用半群表示对Stein方程的解，我们使用从随机演算的工具估计溶液的衍生物，从而在Wasserstein距离上产生了结合。我们首先假设Bakry-Emery-Ricci张量在下面的正常数界定，之后我们分别处理紧凑型歧管上均匀近似的情况。这些结果的应用当前正在开发中，并将出现在随后的文章中。
In this article, we present the theoretical basis for an approach to Stein's method for probability distributions on Riemannian manifolds. Using a semigroup representation for the solution to the Stein equation, we use tools from stochastic calculus to estimate the derivatives of the solution, yielding a bound on the Wasserstein distance. We first assume the Bakry-Emery-Ricci tensor is bounded below by a positive constant, after which we deal separately with the case of uniform approximation on a compact manifold. Applications of these results are currently under development and will appear in a subsequent article.
