Limits for Partial Maxima of Gaussian Random Vectors

TL;DR

This paper establishes almost sure limit theorems for the partial maxima of norms of Gaussian random vectors in Banach spaces, advancing understanding of their asymptotic behavior.

Contribution

It introduces new almost sure limit theorems for partial maxima of Banach-valued Gaussian vectors, a novel extension in the field.

Findings

Almost sure convergence of partial maxima norms

Extension of classical results to Banach-valued Gaussian vectors

New techniques for analyzing maxima in infinite-dimensional spaces

Abstract

We obtain almost sure limit theorems for partial maxima of norms of a sequence of Banach-valued Gaussian random variables.