Statistica Sinica 19 (2009), 1665-1682
SERIES REPRESENTATIONS FOR MULTIVARIATE
GENERALIZED GAMMA PROCESSES VIA
A SCALE INVARIANCE PRINCIPLE
Hemant Ishwaran and Mahmoud Zarepour
Cleveland Clinic and University of Ottawa
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 Lévy processes with given marginals. Some
important special cases are bivariate 
-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.
Key words and phrases: Correlated process, easure,
G-measure.