The maximum principle for stochastic control with partial information

In this paper a Pontryagin-type maximum principle is given for the following stochastic optimal control problem: the state of the system satisfies (i.e. is a weak solution of) an Ito equation with controlled drift and possibly degenerate diffusion coefficients; the controls available are functions of noise-corrupted observations of the state, and the cost to be minimized is the expected value of an integral cost plus a terminal cost. The proof of the Maximum Principle is given elsewhere; here we only state it carefully and then we apply it to the example of the Linear Regulator.