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Some duality results for a class of multivariate semi-markov processes

Published online by Cambridge University Press:  14 July 2016

J. Janssen  and
J. M. Reinhard
J. Janssen*
Affiliation:
Université Libre de Bruxelles
J. M. Reinhard*
Affiliation:
Université Libre de Bruxelles
*
∗Postal address: Departement de Mathématique, Université Libre de Bruxelles, C.P. 210, Campus Plaine, Boulevard du Triomphe, B-1050 Bruxelles, Belgium.
∗Postal address: Departement de Mathématique, Université Libre de Bruxelles, C.P. 210, Campus Plaine, Boulevard du Triomphe, B-1050 Bruxelles, Belgium.
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Abstract

The duality results well known for classical random walk and generalized by Janssen (1976) for (J-X) processes (or sequences of random variables defined on a finite Markov chain) are extended to a class of multivariate semi-Markov processes. Just as in the classical case, these duality results lead to connections between some models of risk theory and queueing theory.

Keywords

MULTIVARIATE SEMI-MARKOV PROCESSESDUALITYWAITING TIMES FOR QUEUES WITH MANY SERVERSRISK THEORY FOR SEVERAL TYPES OF CLAIMS
Type
Research Paper
Information
Journal of Applied Probability , Volume 19 , Issue 1 , March 1982 , pp. 90 - 98
Copyright
Copyright © Applied Probability Trust 1982 

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References

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