Reverse-time modeling, optimal control and large deviations

A connection between deterministic optimal control and large deviations theory has been known for a number of years, whereby the optimal performance index provides information about exit times of stable systems excited by noise, and the optimal trajectory provides information about exit trajectories asymptotically as the scalar multiplying the noise tends to zero. In this paper, a further connection is made to reverse-time modeling of stationary diffusions and linear, stationary, Gauss-Markov discrete-time systems, in which the drift part of the reverse-time model has the same trajectories as the closed loop system resulting from the solution of the same optimal control problem as used for the previous connection.