Telegraph process in the bounded domain with absorbing lower boundary and reflecting with delay upper boundary

TL;DR

This paper analyzes a one-dimensional telegraph process within a bounded domain featuring an absorbing lower boundary and a reflecting delay upper boundary, deriving its distribution via Laplace transforms.

Contribution

It introduces a novel model of the telegraph process with mixed boundary conditions and provides explicit distribution formulas in Laplace transform form.

Findings

Distribution expressed in Laplace transforms

Characterization of boundary behavior in the process

New insights into process dynamics with mixed boundaries

Abstract

We study the asymmetric one-dimensional telegraph process in the bounded domain. Lower boundary is absorbing and upper boundary is reflecting with delay. Point stays in the upper boundary until switch of regime occurs. We obtain the distribution of this process in terms of Laplace trasforms.