Large Deviations of continuous Gaussian processes: from small noise to small time

TL;DR

This paper studies the probability of rare events in continuous Gaussian processes over small time intervals, providing a general method to derive large deviation principles beyond self-similar cases, with various examples.

Contribution

It introduces a new general procedure to obtain large deviation principles in small time for Gaussian processes, extending beyond self-similar cases.

Findings

Developed a method to derive large deviation principles in small time

Extended analysis to non-self-similar Gaussian processes

Provided multiple motivating examples

Abstract

We investigate the Large Deviation behavior in small time of continuous Gaussian processes. We introduce a general procedure allowing to derive Large Deviation Principles in small time starting from the well understood context of Large Deviation Principles with a small parameter, going beyond the self-similar case. Several motivating examples are also treated.