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April 2002 A recursive method for functionals of Poisson processes
Dragan Banjevic, Hemant Ishwaran, Mahmoud Zarepour
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Bernoulli 8(3): 295-311 (April 2002).


Functionals of Poisson processes arise in many statistical problems. 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. We describe a simple recursive method that is useful for characterizing Poisson process functionals and requires only the use of conditional probability. Applications of this technique to convex hulls, extremes, stable measures, infinitely divisible random variables and Bayesian nonparametric priors are discussed.


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Dragan Banjevic. Hemant Ishwaran. Mahmoud Zarepour. "A recursive method for functionals of Poisson processes." Bernoulli 8 (3) 295 - 311, April 2002.


Published: April 2002
First available in Project Euclid: 8 March 2004

zbMATH: 1008.60067
MathSciNet: MR2003H:60069

Keywords: convex hulls , Dirichlet process , Extremes , gamma process , Infinitely divisible random variables , Point processes , Stable processes

Rights: Copyright © 2002 Bernoulli Society for Mathematical Statistics and Probability

Vol.8 • No. 3 • April 2002
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