Weak convergence for generalized semi-Markov processes

A. Hordijk and R. Schassberger

Stochastic Processes and their Applications, 1982, vol. 12, issue 3, 271-291

Abstract: Generalized semi-Markov schemes were introduced by Matthes in 1962 under the designation 'Bedienungsschemata' (service schemes). They include a large variety of familiar stochastic models. It is shown in this paper that under appropriate regularity conditions the associated stochastic process describing the state at timet,t>=0, and the stationary distribution are continuous functions of the life-times of the active components. The supplementary-variable Markov process is shown to be the limit process of a sequence of discrete-state-process obtained through approximating the life-time distributions by mixtures of Erlang distributions and measuring ages and residual life-times in phases. This approach supplements the phase method.

Date: 1982
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