Phase Merging of Semi-Markov Processes

Abstract

The algorithms of phase merging (phase averaging) for the semi-Markov processes and semi-Markov random evolutions are based on the inversion limit theorems for the perturbed invertibly reducible operators (see Korolyuk and Turbin [2]). In both cases, the role of invertibly reducible operator is played the generating operator Q = P − I of a uniformly ergodic Markov chain with the operator of transition probabilities P (see Section 1.4). In the algorithms of phase merging for the semi-Markov processes, the perturbations are given by bounded operators, while in the case of the semi-Markov random evolutions these are closed densely defined operators.