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June, 1957 On Infinitely Divisible Random Vectors
Meyer Dwass, Henry Teicher
Ann. Math. Statist. 28(2): 461-470 (June, 1957). DOI: 10.1214/aoms/1177706974


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.


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Meyer Dwass. Henry Teicher. "On Infinitely Divisible Random Vectors." Ann. Math. Statist. 28 (2) 461 - 470, June, 1957.


Published: June, 1957
First available in Project Euclid: 27 April 2007

zbMATH: 0078.31303
MathSciNet: MR91550
Digital Object Identifier: 10.1214/aoms/1177706974

Rights: Copyright © 1957 Institute of Mathematical Statistics

Vol.28 • No. 2 • June, 1957
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