NECESSARY CONDITIONS OF OPTIMALITY FOR A CLASS OF STOCHASTIC DIFFERENTIAL EQUATIONS ON UMD BANACH SPACES.

In this paper we consider stochastic evolution equations on UMD-Banach spaces. In a recent paper we proved existence of optimal controls. Here in this paper we develop necessary conditions of optimality whereby one can construct the optimal controls. For illustration we use these results to treat the LQR problem in sufficient details under two sets of alternative and distinct assumptions. [ABSTRACT FROM AUTHOR]