## The Annals of Mathematical Statistics

### 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

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