A recursive method for functionals of Poisson processes

摘要: Functionals of Poisson processes arise in many statistical problems. They appear problems involving heavy-tailed distributions the study limiting processes, while Bayesian nonparametric statistics they are used as constructive representations for priors. We describe a simple recursive method that is useful characterizing process functionals requires only use conditional probability. Applications this technique to convex hulls, extremes, stable measures, infinitely divisible random variables and priors discussed.