Log-Level Comparison Principle for Small Ball Probabilities

TL;DR

This paper introduces a new comparison principle for small ball probabilities of Gaussian processes, enabling the derivation of asymptotics for processes with smooth covariances.

Contribution

It presents a novel variant of the comparison principle specifically for logarithmic small ball probabilities of Gaussian processes.

Findings

Established a new comparison principle for Gaussian processes.

Derived small ball asymptotics for processes with smooth covariances.

Enhanced understanding of small ball probability behavior in Gaussian processes.

Abstract

We prove a new variant of comparison principle for logarithmic $L_2$-small ball probabilities of Gaussian processes. As an application, we obtain logarithmic small ball asymptotics for some well-known processes with smooth covariances.