Abstract
We consider a stochastic control problem of a non linear system in which the variable control has two components, the first being absolutely continuous and the second singular. We assume a convex state constraint, a non convex cost criterion and we allow the absolutely continuous component of the control to enter both the drift and diffusion coefficients. The maximum principle is established by using mainly a convex perturbation on a given optimal control. This result generalizes at the same time the result obtained by Cadellinas-Haussman as well as that obtained by Bensoussan.
Subject
Statistics and Probability,Analysis
Reference20 articles.
1. S. Bahlali Doctorat Thesis, Department of mathematics, Batna University - Algeria (2002).
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3. A. Bensoussan. Lecture on stochastic control, in non linear filtering and stochastic control, Lecture notes in mathematics 972, Proc. Cortona, Springer Verlag (1981).
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