## The Annals of Mathematical Statistics

- Ann. Math. Statist.
- Volume 28, Number 2 (1957), 461-470.

### On Infinitely Divisible Random Vectors

#### Abstract

A normally distributed random vector $X$ is well known to be representable by $A \cdot Y$ (in the sense of having identical distributions), where $A$ is a matrix of constants and $Y$ is a random vector whose component random variables are independent. A necessary and sufficient condition for any infinitely divisible random vector to be so representable is given. The limiting case is discussed as are connections with the multivariate Poisson distribution and stochastic processes.

#### Article information

**Source**

Ann. Math. Statist., Volume 28, Number 2 (1957), 461-470.

**Dates**

First available in Project Euclid: 27 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoms/1177706974

**Digital Object Identifier**

doi:10.1214/aoms/1177706974

**Mathematical Reviews number (MathSciNet)**

MR91550

**Zentralblatt MATH identifier**

0078.31303

**JSTOR**

links.jstor.org

#### Citation

Dwass, Meyer; Teicher, Henry. On Infinitely Divisible Random Vectors. Ann. Math. Statist. 28 (1957), no. 2, 461--470. doi:10.1214/aoms/1177706974. https://projecteuclid.org/euclid.aoms/1177706974