Information Divergences and Likelihood Ratios for Poisson Processes and Point Patterns

This article develops an analytical framework for studying information divergences and likelihood ratios associated with Poisson processes and point patterns on general measurable spaces. The main results include explicit analytical formulas for Kullback–Leibler divergences, Rényi divergences, Hellinger distances, and likelihood ratios of the laws of Poisson point patterns in terms of their intensity measures.