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

We consider a stationary and isotropic spatial point process whose a realisation 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.

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