The Cauchy-Schwarz divergence for poisson point processes

Information theoretic divergences are fundamental tools used to measure the difference between the information conveyed by two random processes. In this paper, we show that the Cauchy-Schwarz divergence between two Poisson point processes is the half the squared L
²
-distance between their respective intensity functions. Moreover, this can be evaluated in closed form when the intensities are Gaussian mixtures.