Hitting time for one class of Gaussian proccesses

TL;DR

This paper introduces a method to compute hitting probabilities for Gaussian integrators, including non-Markov processes, using second quantization to derive series representations.

Contribution

It presents a novel approach employing second quantization to analyze hitting probabilities of Gaussian integrators, extending applicability beyond Markov processes.

Findings

Derived series representations for hitting probabilities

Applicable to non-Markov Gaussian integrators

Provides a new analytical tool for Gaussian process analysis

Abstract

In this paper we propose the method to find the hitting probabilities for Gaussian integrators. Using second quantization we obtain the sseries representation for such probabilities despite the fact that integrators can be non-Markov processes.