Electron. J. Diff. Equ.,
Vol. 2010(2010), No. 97, pp. 113.
Filippov approach in stochastic maximum principle without
differentiability assumptions
Mokhtar Hafayed
Abstract:
In this article, we establish necessary conditions for optimality in
stochastic control of systems governed by stochastic differential
equations with nonsmooth coefficients. The approach used is based
on the approximation of the nonsmooth coefficient by smooth one
which generate a sequence of smooth control problems.
Ekeland's variational principle is then applied to obtain a sequence
of nearly optimal controls which satisfy necessary conditions for
near optimality. By using the generalized notion of Filippov's
solutions and the stable convergence, we obtain an explicit
formula for the adjoint process and the inequality between the
Hamiltonians, on a good extension of the initial filtered probability
space.
Submitted April 15, 2010. Published July 15, 2010.
Math Subject Classifications: 60H10, 34F05.
Key Words: Stochastic differential equation; generalized Filippov's
solutions; optimal control; maximum principlel Ekeland's
variational principle.
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Mokhtar Hafayed
Laboratory of Applied Mathematics, University of MedKhider
PO Box 145, Biskra (7000), Algeria
email: hafa.mokh@yahoo.com

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