A recursive method for functionals of Poisson processes

Dragan Banjevic, Hemant Ishwaran, Mahmoud Zarepour

Research output: Contribution to journalArticle

5 Scopus citations

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 that 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.

Original languageEnglish (US)
Pages (from-to)295-311
Number of pages17
JournalBernoulli
Volume8
Issue number3
StatePublished - Jun 1 2002
Externally publishedYes

Keywords

  • Convex hulls
  • Dirichlet process
  • Extremes
  • Gamma process
  • Infinitely divisible random variables
  • Point processes
  • Stable processes

ASJC Scopus subject areas

  • Statistics and Probability

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    Banjevic, D., Ishwaran, H., & Zarepour, M. (2002). A recursive method for functionals of Poisson processes. Bernoulli, 8(3), 295-311.