Dynamic programming equations of stochastic optimal control in banach space

Abstract

In this paper we study the dynamic programming equation (Bellman equation) in Banach space, arising from optimal control problem for stochastic systems driven by a cylindrical Brownian motion, a generalization of white noise in infinite dimensions. A direct method which was introduced by Da Prato in [3,1988] is further developed to prove the existence of mild solutions for the semilinear parabolic equations