Stochastic control with partial observations and no recall

We study stochastic control problems with partial observations. At each point in time the state observation is disturbed by some noise, and the control has to be based on these noisy observations. In the problem that we study, the no recall model, the control can only use the current observation. We formulate an additional model where policies are allowed to use full state observation. A new method is used to prove the equivalence of the original and the additional model. We illustrate the result with a simple example