Large deviations for perturbed Gaussian processes and logarithmic asymptotic estimates for some exit probabilities

TL;DR

This paper studies large deviations for non-Gaussian processes derived from Gaussian processes, providing asymptotic estimates for exit probabilities from specific regions, enhancing understanding of rare event probabilities in perturbed Gaussian systems.

Contribution

It introduces large deviation results for perturbed Gaussian processes and derives asymptotic estimates for exit probabilities, extending classical Gaussian large deviation principles.

Findings

Large deviation principles for non-Gaussian perturbations of Gaussian processes

Logarithmic asymptotic estimates for exit probabilities from halfspaces and quadrants

Corollaries extending the main large deviation results

Abstract

The main results in this paper concern large deviations for families of non-Gaussian processes obtained as suitable perturbations of continuous centered multivariate Gaussian processes which satisfy a large deviation principle. We present some corollaries and, as a consequence, we obtain logarithmic asymptotic estimates for exit probabilities from suitable halfspaces and quadrants.