Bernoulli

  • Bernoulli
  • Volume 8, Number 3 (2002), 295-311.

A recursive method for functionals of Poisson processes

Dragan Banjevic, Hemant Ishwaran, and Mahmoud Zarepour

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Abstract

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.

Article information

Source
Bernoulli, Volume 8, Number 3 (2002), 295-311.

Dates
First available in Project Euclid: 8 March 2004

Permanent link to this document
https://projecteuclid.org/euclid.bj/1078779872

Mathematical Reviews number (MathSciNet)
MR2003h:60069

Zentralblatt MATH identifier
1008.60067

Keywords
convex hulls Dirichlet process extremes gamma process infinitely divisible random variables point processes stable processes

Citation

Banjevic, Dragan; Ishwaran, Hemant; Zarepour, Mahmoud. A recursive method for functionals of Poisson processes. Bernoulli 8 (2002), no. 3, 295--311. https://projecteuclid.org/euclid.bj/1078779872


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