On the semi-Markovian random walk process with reflecting and delaying barriers

Abstract

In this paper, a semi-Markovian random walk process X(t) with reflecting barrier on the zero-level and delaying barrier on the beta(beta>0 )-level and the first falling moment of the process into the delaying barrier, (gamma), are considered. Some probability characteristics of gamma, such as its distribution function, moment generating function and expected value are calculated.