Giuseppina Guatteri
Published 2008-07-19, updated 2011-02-22Version 3
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.
Stochastic maximum principle for sub-diffusions and its applications
Time regularity of Lévy-type evolution in Hilbert spaces and of some $α$-stable processes
Hörmander's theorem for stochastic partial differential equations
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