  This paper revisits the question of duality between minimum variance
estimation and optimal control first described for the linear Gaussian case in
the celebrated paper of Kalman and Bucy. A duality result is established for
nonlinear filtering, mirroring closely the original Kalman-Bucy duality of
control and estimation for linear systems. The result for the finite
state-space continuous time Markov chain is presented. It's solution is used to
derive the classical Wonham filter.
