Comparison theorems for the small ball probabilities of Gaussian processes in weighted $L_2$-norms

TL;DR

This paper establishes comparison theorems for small ball probabilities of Green Gaussian processes in weighted L2 norms, providing sharp asymptotics for many classical processes under broad conditions.

Contribution

It introduces new comparison theorems and derives precise small ball asymptotics for Gaussian processes in weighted norms, extending existing results to more general settings.

Findings

Comparison theorems for small ball probabilities

Sharp asymptotics for classical Gaussian processes

Applicability under general weight assumptions

Abstract

We prove comparison theorems for small ball probabilities of the Green Gaussian processes in weighted $L_2$-norms. We find the sharp small ball asymptotics for many classical processes under quite general assumptions on the weight.