Stochastic Maximum Principle for a PDEs with noise and control on the boundary

Details Stochastic Maximum Principle for a PDEs with noise and control on the boundary Stochastic Maximum Principle for a PDEs with noise and control on the boundary

2008-07-19

arxiv.org/abs/0807.3096v3

Mathematics

Probability

15pgs

Scientific paper

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.

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