Series representations for multivariate generalized gamma processes via a scale invariance principle

Hemant Ishwaran, Mahmoud Zarepour

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

We introduce a scale invariance property for Poisson point processes and use this property to define a series representation for a correlated bivariate gamma process. This approach is quite general and can be used to define other types of multidimensional Levy processes with given marginals. Some important special cases are bivariate G-processes, bivariate variance gamma processes and multivariate Dirichlet processes. Using the scale invariance principle we show how to construct simple approximations to these multivariate processes.

Original languageEnglish
Pages (from-to)1665-1682
Number of pages18
JournalStatistica Sinica
Volume19
Issue number4
StatePublished - Oct 1 2009
Externally publishedYes

Fingerprint

Gamma Process
Scale Invariance
Invariance Principle
Series Representation
Poisson Point Process
Dirichlet Process
Lévy Process
Approximation
Gamma process
Scale invariance
Dirichlet process
Point process
Variance gamma
Lévy process

Keywords

  • Correlated process
  • Easure
  • G-measure

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Series representations for multivariate generalized gamma processes via a scale invariance principle. / Ishwaran, Hemant; Zarepour, Mahmoud.

In: Statistica Sinica, Vol. 19, No. 4, 01.10.2009, p. 1665-1682.

Research output: Contribution to journalArticle

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