The purpose of this paper is to study some statistical problems : parameter estimation, binary detection , change detection (disorder problem), etc. for partially observed diiusion processes, using the likelihood approach. It is shown that the stochastic PDE related to the state estimation problem, provides also a way to compute the likelihood function/ratio. A recent result on consistency of t...

Traditional methods of nonparametric function estimation (splines, kernels and especially wavelet lters) usually produce arti cial features/spurious oscillations. Piecewise convex function estimation seeks to reliably estimate the geometric shape of the unknown function. We outline how piecewise convex tting may be applied to signal recovery, instantaneous frequency estimation, surface reconstr...