Near Optimal Finite Model POMDP Approximation of Controlled Diffusion with Partial Information

We study continuous-time stochastic control problems under partial information. Our main contributions are the following: (i) We show near optimality, under finite horizon as well as discounted infinite horizon cost criteria, of piece-wise constant control policies obtained via solutions to discrete-time partially observable Markov decision process (POMDP) approximations, constructed via Euler-Maruyama approximations of both state and observation processes; (ii) we obtain several regularity properties of such POMDP approximate models; and (iii) using these regularity properties, we arrive at near optimal finite model approximations. (iv) These culminate into our main result which is that an optimal solution for the approximate finite POMDP model is near optimal for the original diffusion with partial information.