Bang-bang controls of point processes
- 1 June 1976
- journal article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 8 (2) , 385-394
- https://doi.org/10.2307/1425910
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
This publication has 2 references indexed in Scilit:
- Multivariate point processes: predictable projection, Radon-Nikodym derivatives, representation of martingalesProbability Theory and Related Fields, 1975
- Intégrales stochastiques par rapport aux martingales localesPublished by Springer Nature ,1970