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.
MADEN, SELAHATTİN (2001) "On the Semi-Markovian Random Walk Process with Reflecting and Delaying Barrriers," Turkish Journal of Mathematics: Vol. 25: No. 2, Article 2. Available at: https://journals.tubitak.gov.tr/math/vol25/iss2/2