Maximum principle for optimal control of stochastic partial differential equations

We consider a stochastic maximum principle of optimal control for a control problem associated with a stochastic partial differential equation driven by a continuous martingale, which takes its values in a separable Hilbert space, and a random unbounded linear operator. We derive necessary conditions of optimality for this control problem without a convexity assumption on the control domain, and also when the control variable is allowed to enter in the martingale part of the equation. Linear and nonlinear equations are considered in this study