On the Semi-Markovian Random Walk Process with Reflecting and Delaying Barrriers


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.

Keywords: Semi-Markovian random walk, reflecting barrier, delaying barrier, expected value.

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