A recursive method for functionals of Poisson processes. (English) Zbl 1008.60067

From the authors’ abstract: Functionals of Poisson processes arise in many statistical problems. For example, they appear in problems involving heavy-tailed distributions in the study of limiting processes, while in Bayesian nonparametric statistics they are used as constructive representations for nonparametric priors. The authors describe a simple recursive method that is useful for characterizing Poisson process functionals that requires only the use of conditional probabilities. Applications of this technique to convex hulls, extremes, stable measures, infinitely divisible random variables and Bayesian nonparametric priors are discussed.
Reviewer: V.Schmidt (Ulm)


60G51 Processes with independent increments; Lévy processes