Temporal Cox Process with Folded Normal Intensity

In this work, the case of a Cox Process with Folded Normal Intensity (CP-FNI), in which the intensity is given by (Formula presented.), where (Formula presented.) is a stationary Gaussian process, is studied. Here, two particular cases are dealt with: (i) when the process (Formula presented.) constitutes a family of independent random variables and with a common probability law (Formula presented.), and (ii) the case in which (Formula presented.) is a second order stationary process, with exponential type covariance function. In these cases, we observe that the properties of the Gaussian process (Formula presented.) are naturally transferred to the intensity (Formula presented.) and that very analytical results are achievable from the analytical point of view for the point process (Formula presented.). Finally, some simulations are presented in order to appreciate what type of counting phenomena can be modeled by these cases of CP-FNI. In particular, it is interesting to see how the trajectories show a tendency of the events to be grouped in certain periods of time, also leaving long periods of time without the occurrence of events.