On Critical Points for Gaussian Vectors with Infinitely Divisible Squares

TL;DR

This paper explores the conditions under which a three-dimensional Gaussian vector with infinitely divisible squares maintains its infinite divisibility after perturbations, providing insights into the stability of such vectors.

Contribution

It introduces criteria for perturbations that preserve infinite divisibility in Gaussian vectors with infinitely divisible squares.

Findings

Identifies specific perturbation bounds for infinite divisibility

Provides theoretical conditions for stability of Gaussian vectors

Enhances understanding of Gaussian vector perturbations

Abstract

Investigates the size of the perturbation to the zero mean three dimensional Gaussian vector with infinitely divisible squares so that the infinite divisibility is retained.