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Bang-bang controls of point processes

Published online by Cambridge University Press:  01 July 2016

P. Brémaud
P. Brémaud*
Affiliation:
CEREMADE, Université de Paris IX (Dauphine)
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Abstract

In this paper, we consider the problem of controlling the intensity of a point process in order to maximize the probability that the number of points in a fixed interval equals a given integer, under the constraint that the intensity belong to some closed interval of R+.

The problem is stated as a problem of optimization on the set of probabilities over the basic measurable space of point processes, and shown to be equivalent to a problem of deterministic control. Structural results concerning the set of optimal solutions are given. The existence of the latter is proven; the control is shown to be bang-bang and a complete solution can be obtained by application of Pontryagin's Maximum Principle.

Keywords

POINT PROCESSQUEUING PROCESSMARTINGALEPREDICTABLE PROCESSSTOCHASTIC INTEGRALOPTIMAL CONTROLBANG-BANG CONTROL
Type
Research Article
Information
Advances in Applied Probability , Volume 8 , Issue 2 , June 1976 , pp. 385 - 394
Copyright
Copyright © Applied Probability Trust 1976 

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References

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