Shot noise weighted processes: a new family of spatial point processes

Abstract

This paper proposes a new family of spatial point processes defined by their density with respect to a Poisson process on a bounded window. The density will be specified in terms of functionals of shot noise processes with various influence functions, for example the coverage function. Stability, Markov properties, stationary extensions and limit behaviour are studied. Examples and simulated realisations are given to indicate the applicability of shot noise weighted processes.

Keywords:

• coverage function
• Markov point process
• spatial interaction
• shot noise