Weak convergence for generalized semi-Markov processes
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.
Year of publication: |
1982
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Authors: | Hordijk, A. ; Schassberger, R. |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 12.1982, 3, p. 271-291
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Publisher: |
Elsevier |
Saved in:
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