Toolbox: Gaussian comparison on Eucledian balls

TL;DR

This paper characterizes the differences between multivariate Gaussian measures on Euclidean balls, providing bounds on the Kolmogorov distance, which enhances understanding of Gaussian measure comparisons.

Contribution

It introduces a new characterization of Gaussian measure differences on Euclidean balls, aiding in bounding the Kolmogorov distance.

Findings

Derived bounds for Gaussian measure differences

Provided tools for Kolmogorov distance estimation

Enhanced understanding of Gaussian measure comparisons

Abstract

In the work a characterization of difference of multivariate Gaussian measures is found on the family of centered Eucledian balls. In particular, it helps to bound corresponding Kolmogorov distance.