Adapted kriging to predict the intensity of partially observed point process data

We consider a stationary and isotropic spatial point process whose realization is observed within a large window. We assume it to be driven by a stationary random field U. In order to predict the local intensity of the point process, λ(x|U), we propose to define the first- and second-order characteristics of a random field, defined as the regularized counting process, from the ones of the point process and to interpolate the local intensity by using a kriging adapted to the regularized process.