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 language | English |
|---|---|
| Pages (from-to) | 1665-1682 |
| Number of pages | 18 |
| Journal | Statistica Sinica |
| Volume | 19 |
| Issue number | 4 |
| State | Published - Oct 1 2009 |
| Externally published | Yes |
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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 journal › Article
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TY - JOUR
T1 - Series representations for multivariate generalized gamma processes via a scale invariance principle
AU - Ishwaran, Hemant
AU - Zarepour, Mahmoud
PY - 2009/10/1
Y1 - 2009/10/1
N2 - 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.
AB - 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.
KW - Correlated process
KW - Easure
KW - G-measure
UR - http://www.scopus.com/inward/record.url?scp=73249128998&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=73249128998&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:73249128998
VL - 19
SP - 1665
EP - 1682
JO - Statistica Sinica
JF - Statistica Sinica
SN - 1017-0405
IS - 4
ER -