Markov skeleton processes

Abstract

A new class of stochastic processes—Markov skeleton processes is introduced, which have the Markov property on a series of random times. Markov skeleton processes include minimalQ processes, Doob processes,Q processes of order one, semi-Markov processes[1], piecewise determinate Markov processes[2], and the input processes, the queuing lengths and the waiting times of the system G1/G/1, as particular cases. First, the forward and backward equations are given, which are the criteria for the regularity and the formulas to compute the multidimensional distributions of the Markov skeleton processes. Then, three important cases of the Markov skeleton processes are studied: the (H, G, II)-processes, piecewise determinate Markov skeleton processes and Markov skeleton processes of Markov type. Finally, a vast vistas for the application of the Markov skeleton processes is presented.