An approximation method for stochastic control problems with partial observation of the state — a method for constructing ∈-optimal controls

We consider a continuous-time stochastic control problem with partial observations. Given some assumptions, we reduce the problem in successive approximation steps to a discrete-time, complete-observation, stochastic control problem with a finite number of possible states and controls. For the latter problem an optimal control can always be explicitly computed. Convergence of the approximations is shown, which in turn implies that an optimal control for the last-stage approximating problem is ∈-optimal for the original problem.