论文标题
对Riemannian流形的Stein方法的扩散方法
A diffusion approach to Stein's method on Riemannian manifolds
论文作者
论文摘要
我们详细介绍了一种开发Stein方法的方法，该方法是针对Riemannian歧管$ \ Mathbf M $界定的概率度量界定整体指标的。我们的方法利用了$ \ mathbf m $扩散的生成器与目标不变度量及其表征Stein运算符之间的关系。我们考虑了一对具有不同起点的扩散，并通过对两对之间的距离过程进行分析，得出了Stein因子，该因子将解决方案绑定到Stein方程及其衍生物。 Stein因子包含与曲率相关的术语，并减少到当前可用于$ \ Mathbb r^m $的术语，此外，暗示$ \ Mathbb r^m $的界限在$ \ Mathbf m $是平坦的歧管时保持有效
We detail an approach to develop Stein's method for bounding integral metrics on probability measures defined on a Riemannian manifold $\mathbf M$. Our approach exploits the relationship between the generator of a diffusion on $\mathbf M$ with target invariant measure and its characterising Stein operator. We consider a pair of such diffusions with different starting points, and through analysis of the distance process between the pair, derive Stein factors, which bound the solution to the Stein equation and its derivatives. The Stein factors contain curvature-dependent terms and reduce to those currently available for $\mathbb R^m$, and moreover imply that the bounds for $\mathbb R^m$ remain valid when $\mathbf M$ is a flat manifold
