A multidimensional version of noise stability

TL;DR

This paper extends Borell's noise stability theorem to multivariate Gaussian vectors, leading to new inequalities related to the exit times of the Ornstein-Uhlenbeck process, enhancing understanding of Gaussian measures and stochastic processes.

Contribution

It provides a multivariate generalization of Borell's noise stability theorem, connecting it to inequalities for Ornstein-Uhlenbeck process exit times.

Findings

Generalized noise stability to multivariate Gaussian vectors

Derived new inequalities for Ornstein-Uhlenbeck exit times

Reconnected Gaussian stability with stochastic process behavior

Abstract

We give a multivariate generalization of Borell's noise stability theorem for Gaussian vectors. As a consequence we recover two inequalities, also due to Borell, for exit times of the Ornstein-Uhlenbeck process.