A general maximum principle for partially observed stochastic evolution control systems

In this paper, we study an optimal control problem of partially observed stochastic evolution equation control system. The observation process is an infinite-dimensional stochastic process, and the control variable is allowed to enter the diffusion term of the state process and the drift term of the observation process. The control domain need not be convex. Combined with Girsanov theorem, we establish the related stochastic maximum principle in the sense of transposition solution.