Maximum likelihood estimation of a nonparametric signal in white noise by optimal control

We study extremal problems related to nonparametric maximum likelihood estimation (MLE) of a signal in white noise. The aim is to reduce these to standard problems of optimal control which can be solved by iterative procedures. This reduction requires a preliminary data smoothing; stability theorems are proved which justify such an operation on the data as a perturbation of the originally sought nonparametric (nonlinear) MLE. After this, classical optimal control problems appear; in the basic case of a signal with bounded first derivative one obtains the well-known problem of the optimal road profile.