ABSTRACT
The goal of this paper is to present a full optimal feedback synthesis along with well-posedness of the stochastic Riccati equation for an infinite dimensional stochastic linear quadratic control problem with unbounded control operators. The finite dimensional counterpart of this problem is well known in the literature; see, for instance, [7] and [15]. The infinite dimensional problem has been studied in the literature within the context of analytic semigroups eAt and the corresponding stochastic processes driven by relatively (with respect to A) bounded control operators B [4,6]. Our aim is to extend the theory presented in [4] and [6] to a larger class of dynamics that are not analytic.
