论文标题
在随机过程的分布的沃斯坦斯坦变形下，Euler和Betti曲线稳定
Euler and Betti curves are stable under Wasserstein deformations of distributions of stochastic processes
论文作者
论文摘要
在$ d $维的紧凑riemannian流形上定义的随机过程的Euler和Betti曲线，几乎肯定在Sobolev space $ w^{n，s}（x，x，x，x，\ mathbb {r}）$（带有$ d <n $）稳定在赛义者的分布下是稳定的。此外，显示所有$ p> \ frac {d} {n} $的持久图显示，瓦斯恒星的稳定性显示为依赖于$ w^{n，s}（x，x，x，\ mathbb {r}）$的持续图。
Euler and Betti curves of stochastic processes defined on a $d$-dimensional compact Riemannian manifold which are almost surely in a Sobolev space $W^{n,s}(X,\mathbb{R})$ (with $d<n$) are stable under perturbations of the distributions of said processes in a Wasserstein metric. Moreover, Wasserstein stability is shown to hold for all $p>\frac{d}{n}$ for persistence diagrams stemming from functions in $W^{n,s}(X,\mathbb{R})$.
