The estimate of potential in stochastic Schrödingerʹs equation

We consider a generalized Gaussian random field given by the stochastic Schrödingerʹs equation (−Δ + C)ξ = η, in . When the dimension of our initial space Rq is greater than 4, we can estimate the potential C with probability 1 observing ξ in an arbitrary small neighbourhood of a point t G. In the case when q < 4 and homogeneous boundary values are suppose, we can determine the Radon-Nikodym derivative of measures corresponding to different constant potentials. In the case q = 1, one can solve explicitly the maximum-likelihood equation.