Clarification of basic factorization identity for the almost semi-continuous latticed Poisson processes on the Markov chains

Abstract

Let $\{\xi(t), x(t)\}$ be a homogeneous semicontinuous lattice Poisson process on the Markov chain. The jumps of one sign are geometrically distributed, and jumps of the opposite sign are arbitrary latticed distribution. For a such processes the relations for the components of two-sided matrix factorization are established. This relations define the moment genereting functions for extremums of the process and their complements.