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 the spatio-temporal $K$-function. We further discuss its explicit form under some specific model assumptions and derive ratio-unbiased estimators. We finally illustrate the use of our statistic in practice