Laplace Transform of the Distribution of the Semi-Markov Walk Process with a Positive Drift, Negative Jumps, and a Delay Screen at Zero

Abstract

In this paper, we investigate the process of semi-Markov random walk with a positive drift, negative jumps, and a delay screen at zero. Explicit forms are found of the Laplace transform in time, the Laplace-Stieltjes transform by the state (phase) of the conditional and unconditional distributions of the process states, and the explicit form of the Laplace-Stieltjes transform of the ergodic distribution of the process.