Asymptotic results for the absorption time of telegraph processes with a non-standard barrier at the origin

TL;DR

This paper investigates the asymptotic behavior of the absorption time in a generalized telegraph process with a non-standard barrier, extending previous work by analyzing large and moderate deviations for a broader class of distributions.

Contribution

It introduces a generalized model of the telegraph process with a light-tailed distribution for the number of visits, and derives new asymptotic deviation results.

Findings

Derived large deviation principles for the generalized model.

Established moderate deviation results extending previous asymptotic analysis.

Provided insights into the tail behavior of absorption times in telegraph processes.

Abstract

A telegraph process with an elastic barrier at the origin was studied in [5]; in particular the number of visits of the origin before the absorption is a geometric distributed random variable M. Some asymptotic results (large and moderate deviations) for that model were obtained in [17]. In this paper we study large and moderate deviations for a generalized model where M is a light-tailed distributed random variable.