Large deviations for conditionally Gaussian processes: estimates of level crossing probability

TL;DR

This paper extends large deviation theory to conditionally Gaussian processes and provides estimates for their level crossing probabilities, broadening the applicability of Gaussian process analysis.

Contribution

It introduces a new large deviation framework for conditionally Gaussian processes and derives level crossing probability estimates, expanding existing Gaussian process theory.

Findings

Extended large deviation principles to conditionally Gaussian processes

Derived explicit estimates for level crossing probabilities

Broadened the scope of Gaussian process analysis

Abstract

The problem of (pathwise) large deviations for conditionally continuous Gaussian processes is investigated. The theory of large deviations for Gaussian processes is extended to the wider class of random processes -- the conditionally Gaussian processes. The estimates of level crossing probability for such processes are given as an application.