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Stochastic ordering of random processes with an imbedded point process

Published online by Cambridge University Press:  14 July 2016

François Baccelli
François Baccelli*
Affiliation:
INRIA
*
∗ Postal address: INRIA, Sophia-Antipolis, 2004 Rte des Lucioles, 06565 Valbonne Cedex, France.
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Abstract

We introduce multivariate partial orderings related with the Palm and time-stationary probabilities of a point process. Using these orderings, we give conditions for the monotonicity of a random sequence, with respect to some integral stochastic ordering, to be inherited with a continuous time process in which this sequence is imbedded. This type of inheritance is also discussed for the property of association.

Keywords

INTEGRAL STOCHASTIC ORDERINGPALM PROBABILITIESSTOCHASTIC PROCESSES WITH AN IMBEDDED POINT PROCESSASSOCIATION OF RANDOM VARIABLES
Type
Research Papers
Information
Journal of Applied Probability , Volume 28 , Issue 3 , September 1991 , pp. 553 - 567
Copyright
Copyright © Applied Probability Trust 1991 

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References

[1] Baccelli, F. and Bremaud, P. (1987) Palm Probabilities and Stationary Queues. Lecture Notes in Statistics 41, Springer-Verlag, Berlin.Google Scholar
[2] Baccelli, F. and Bremaud, P. (1991) Elements of Queueing Theory. Springer-Verlag, Berlin. To appear in the Applications of Mathematics Series.Google Scholar
[3] Baccelli, F. and Makowski, A. M. (1989) Queueing models for systems with synchronization constraints. Proc. IEEE 77, 138–161.Google Scholar
[4] Baccelli, F. and Makowski, A. M. (1991) Stochastic orders associated with the forward recurrence time of a renewal process. Submitted for publication.Google Scholar
[5] Barlow, R. E. and Proschan, F. (1975) Statistical Theory of Reliability and Life Testing. Holt Rinehart and Winston, New York.Google Scholar
[6] Franken, P., König, D., Arndt, U. and Schmidt, V. (1981) Queues and Point Processes. Akademie-Verlag, Berlin.Google Scholar
[7] Stoyan, D. (1983) Comparison Methods for Queues and Other Stochastic Models. Wiley, New York.Google Scholar
[8] Strassen, V. (1965) The existence of probability measures with given marginals. Ann. Math. Statist. 36, 423–439.CrossRefGoogle Scholar
[9] Whitt, W. (1985) The renewal-process stationary excess operator. J. Appl. Prob. 22, 156–167.CrossRefGoogle Scholar