Investigation of Laplace-Stieltjes transform for the ergodic distribution of the semi-markov random process with positive tendency, negative jumps and delaying boundary at zero.

Abstract

One of the important problems of stochastic processes theory is to define the Laplace-Stieltjes transform for the ergodic distribution of semi-markov random process. With this purpose, we will investigate the semi-markov random processes with positive tendency, negative jumps and delaying boundary at zero in this article. The Laplace transform on time, Laplace-Stieltjes transform on phase of the conditional and unconditional  distributions and Laplace-Stieltjes transform  of the ergodic distribution are defined. The characteristics of the ergodic distribution will be calculated on the basis of the final results.