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Some EATA properties for marked point processes

Part of: Stochastic processes

Published online by Cambridge University Press:  14 July 2016

D. Kofman  and
H. Korezlioglu
D. Kofman*
Affiliation:
ENST, Paris
H. Korezlioglu*
Affiliation:
ENST, Paris
*
∗Postal address: Networks Department, Ecole Nationale Supérieure des Télécommunications, 46 rue Barrault, 75634 Paris Cedex 13, France.
∗Postal address: Networks Department, Ecole Nationale Supérieure des Télécommunications, 46 rue Barrault, 75634 Paris Cedex 13, France.
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Abstract

We derive an ESTA property for marked point processes similar to Wolff's PASTA property for ordinary (non-marked) point processes, via a stochastic integral approach. This new ESTA property allows us to extend a known result on the conditional PASTA property and to derive an ASTA property for batch arrival processes. We also present an application of our results.

Keywords

MARKED POINT PROCESSESSTOCHASTIC INTENSITYSTOCHASTIC INTEGRALSEATAESTACONDITIONAL PASTAASTABATCH ARRIVALS

MSC classification

Primary: 60G55: Point processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 32 , Issue 4 , December 1995 , pp. 922 - 929
Copyright
Copyright © Applied Probability Trust 1995 

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References

[1] Baccelli, F. and Bremaud, P. (1994) Elements of Queueing Theory, Palm-Martingale Calculus and Stochastic Recurrences. Springer-Verlag, Berlin.Google Scholar
[2] Bremaud, P., Kannurpatti, R. and Mazumdar, R. (1992) Event and time averages: a review. Adv. Appl. Prob. 24, 377–411.CrossRefGoogle Scholar
[3] Bremaud, P. (1981) Point Processes and Queues, Martingale Dynamics. Springer-Verlag, Berlin.CrossRefGoogle Scholar
[4] Dacunha-Castelle, D. and Duflo, M. (1982) Probabilités et Statistiques, Vol. 2: Problèmes à temps mobile. Masson, Paris.Google Scholar
[5] Doob, J. L. (1953) Stochastic Processes. Wiley, New York.Google Scholar
[6] Van Doorn, E. A. and Regterschot, G. J. K. (1988) Conditional PASTA. Operat. Res. Lett. 7, 229–232.CrossRefGoogle Scholar
[7] Jacod, J. (1976) Un théorème de représentation pour les martingales discontinues. Z. Wahrscheinlichkeitsth. 34, 225–244.CrossRefGoogle Scholar
[8] Kabanov, J. M., Liptser, R. S. and Shiryayev, A. N. (1979) Absolute continuity and singularity of locally absolutely continuous probability distributions: I. Math. USSR Sb. 35, 631–679.CrossRefGoogle Scholar
[9] Kofman, D. and Korezlioglu, H. (1993) Loss probabilities and delay and jitter distributions in a finite buffer queue with heterogeneous batch Markovian arrival processes. In Proc. IEEE GLOBECOM'93, Houston, 830–834.CrossRefGoogle Scholar
[10] Lucantoni, D. M. (1991) New results on the single server queue with a batch markovian arrival process,. Stoch. Models 7, 1–46.CrossRefGoogle Scholar
[11] Neuts, M. F. (1979) A versatile Markovian point process. J. Appl. Prob. 16, 764–769.CrossRefGoogle Scholar
[12] Rosenkrantz, W. A. and Simha, R. (1992) Some theorems on conditional Pasta: A stochastic integral approach. Operat. Res. Lett. 11, 173–177.CrossRefGoogle Scholar
[13] Wolff, R. W. (1982) Poisson arrivals see time averages. Operat. Res. 30, 223–231.CrossRefGoogle Scholar