Abstract
Recently Zolezzi, [4] presented a necessary condition for optimality for the problem of optimal control of systems governed by parabolic partial differential equations with a first boundary condition. In this paper, we have developed (Theorem 4.3 and Corollary 4.5) a similar necessary condition for Cauchy problems (unbounded domains) that arise naturally in the optimal control problems of stochastic Ito differential systems with fixed terminal time. For the proof of our results we use several theorems of Aronson [1] which have been slightly modified to suit our requirements.
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