Geodesic
The maximum principle for some nonlinear stochastic control system with variable structure
Teoriâ slučajnyh processov, Tome 16 (2010) no. 1, pp. 1-11.

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Necessary conditions of optimality are derived for the stochastic control problem for a dynamical system with variable structure. The system is described by stochastic differential equations, when a control enters the drift and diffusion coefficients. The maximum principle for some non-linear stochastic control system with endpoint constraint is proved.
Keywords: Variable structure system, nonlinear stochastic differential equations, stochastic optimal control problem, maximum principle, admissible controls, adjoint stochastic differential equations, optimal control problem with constraint, Ekeland variation principle. 
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C. A. Agayeva; Q. U. Abushov. The maximum principle for some nonlinear stochastic control system with variable structure. Teoriâ slučajnyh processov, Tome 16 (2010) no. 1, pp. 1-11. http://geodesic.mathdoc.fr/item/THSP_2010_16_1_a0/

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