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.