### 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 |

### Fingerprint

### Keywords

- Correlated process
- Easure
- G-measure

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty

### Cite this

*Statistica Sinica*,

*19*(4), 1665-1682.

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

Research output: Contribution to journal › Article

*Statistica Sinica*, vol. 19, no. 4, pp. 1665-1682.

}

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 -