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Processus ponctuels et martingales: résultats récents sur la modélisation et le filtrage

Published online by Cambridge University Press:  01 July 2016

P. Brémaud  and
J. Jacod
P. Brémaud*
Affiliation:
CEREMADE, Université Paris IX
J. Jacod
Affiliation:
Université de Rennes
*
∗Adresse actuelle: IRIA/LABORIA, Rocquencourt, France.
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Abstract

This paper contains a review of the results of the martingale approach to point processes and its applications to the theory of dynamical systems (in the engineering sense), mainly estimation problems.

Some of the topics reviewed are: stochastic intensity, absolutely continuous changes of measure, martingale representations, changes of times, filtering, queues, etc.

Keywords

point processqueuing processmartingalepredictable projectionradon-nikodym derivativestieltjes stochastic integralfilteringstochastic intensity
Type
Research Article
Information
Advances in Applied Probability , Volume 9 , Issue 2 , June 1977 , pp. 362 - 416
Copyright
Copyright © Applied Probability Trust 1977 

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