Predicting the intensity of partially observed data from a revisited kriging for point processes

Abstract

We consider a stationary and isotropic spatial point process, whose a realisation is observed within a large window. In order to predict its local intensity, 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 intensity by using a revisited kriging of the regularized process.