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

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.

Keywords

• Conditionally Gaussian processes
• Large deviations
• ruin problem