On the existence of stochastic optimal control of distributed state system Original Research Article

An optimal control problem governed by a semilinear parabolic stochastic differential equation with nonlinear diffusion coefficient is studied and the existence of a quasi-optimal (nonrelaxed) control is proved without assuming convexity of the coefficients. The control state space is not compact and of infinite dimension, the stochastic equation is driven by a cylindrical Brownian motion.