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Stochastic Maximum Principle for a PDEs with noise and control on the boundary (0807.3096v3)
Published 19 Jul 2008 in math.PR, cs.SY, and math.OC
Abstract: In this paper we prove necessary conditions for optimality of a stochastic control problem for a class of stochastic partial differential equations that is controlled through the boundary. This kind of problems can be interpreted as a stochastic control problem for an evolution system in an Hilbert space. The regularity of the solution of the adjoint equation, that is a backward stochastic equation in infinite dimension, plays a crucial role in the formulation of the maximum principle.