Investigation of Some Probabilistic Characteristics of One Class of Semi-Markov Wandering with Delaying Screens

摘要

The process of semi-Markov wandering with delaying screens "b" and "a" (a > b > 0) is constructed by the given sequence of independent and identically distributed random vectors (ξ_i, η_i), i ≥ 1. The integral equation for the Laplace transform by time and the Laplace-Stieltjes transform by the phase of its conditional distribution is derived. If the wandering occurs by a complicated Laplace distribution, the ergodic distribution of the process and its moments are found. Then, the integral equation for the generating function of the conditional distribution of the number of process steps at which it firstly reaches the level a is derived. When the wandering occurs by the simple Laplace distribution, its generating functions and moments are found.