AJ-function for Inhomogeneous Spatio-temporal Point Processes

A J-function for Inhomogeneous Spatio-temporal Point Processes

We propose a new summary statistic for inhomogeneous intensity-reweighted moment stationarity spatio-temporal point processes. The statistic is defined in terms of the n-point correlation functions of the point process, and it generalizes the J -function when stationarity is assumed. We show that our statistic can be represented in terms of the generating functional and that it is related to th...

Spatial and Spatio-temporal Point Processes

The present paper gives the background to point processes in space and time. Some special types of spatial and spatio-temporal models of point processes are introduced with the emphasis to Cox processes. Their basic properties are described and some characteristics are calculated. The simulation of one of these models is shown. Introduction At present, the theory of point processes is well esta...

A Partial Likelihood for Spatio-temporal Point Processes

Spatio-temporal càdlàg functional marked point processes: Unifying spatio-temporal frameworks

This paper defines the class of càdlàg functional marked point processes (CFMPPs). These are (spatio-temporal) point processes marked by random elements which take values in a càdlàg function space, i.e. the marks are given by càdlàg stochastic processes. We generalise notions of marked (spatio-temporal) point processes and indicate how this class, in a sensible way, connects the point process ...

On an application of spatio-temporal point processes