The Partially Observed Stochastic Minimum Principle
J.S. Baras, R. Elliott and M. Kohlmann
SIAM Journal on Control and Optimization, Vol. 27, No. 6, pp. 1279-1292, November 1989.
Using stochastic flows and the generalized differentiation formula of Bismut and Kunita, the change in cost due to a strong variation of an optimal control is explicitly calculated. Differentiating this expression gives a minimum principle in both the partially observed and stochastic open loop situations. In the latter case the equation satisfied by the adjoint process is obtained by applying a martingale representation result.