SERIES REPRESENTATIONS FOR MULTIVARIATE GENERALIZED GAMMA PROCESSES VIA A SCALE INVARIANCE PRINCIPLE
Hemant Ishwaran, Mahmoud Zarepour · 2009
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 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. Key words and phrases: Correlated process, easure, G-measure. 1. Introduction. The univariate gamma process, and its various extensions, plays an important role in a variety of applications. For example, the Dirichlet process, a fundamental prior used in a wide array of Bayesian nonparametric problems, is defined in terms of a gamma process (Ferguson and Klass (1972) and Ferguson