## Bernoulli

• Bernoulli
• Volume 12, Number 1 (2006), 169-189.

### Which multivariate gamma distributions are infinitely divisible?

Philippe Bernardoff

#### Abstract

We define a multivariate gamma distribution on $R n$ by its Laplace transform $( P( -θ ) ) - λ$, $λ >0,$ where

$P ( θ )=∑ T ⊂{ 1,…,n }p T ∏ i ∈Tθ i .$

Under $p { 1,…,n } ≠0$, we establish necessary and sufficient conditions on the coefficients of $P ,$ such that the above function is the Laplace transform of some probability distribution, for all $λ >0,$ thus characterizing all infinitely divisible multivariate gamma distributions on $R n .$

#### Article information

Source
Bernoulli, Volume 12, Number 1 (2006), 169-189.

Dates
First available in Project Euclid: 28 February 2006

https://projecteuclid.org/euclid.bj/1141136656

Mathematical Reviews number (MathSciNet)
MR2202328

Zentralblatt MATH identifier
1101.60008

#### Citation

Bernardoff, Philippe. Which multivariate gamma distributions are infinitely divisible?. Bernoulli 12 (2006), no. 1, 169--189. https://projecteuclid.org/euclid.bj/1141136656

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