The Annals of Probability

On Series Representations of Infinitely Divisible Random Vectors

Jan Rosinski

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Abstract

General results on series representations, involving arrival times in a Poisson process, are established for infinitely divisible Banach space valued random vectors without Gaussian components. Applying these results, various generalizations of LePage's representation are obtained in a unified way. Certain conditionally Gaussian infinitely divisible random vectors are characterized and some problems related to a Gaussian randomization method are investigated.

Article information

Source
Ann. Probab., Volume 18, Number 1 (1990), 405-430.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176990956

Digital Object Identifier
doi:10.1214/aop/1176990956

Mathematical Reviews number (MathSciNet)
MR1043955

Zentralblatt MATH identifier
0701.60004

JSTOR
links.jstor.org

Keywords
B12 E07 Infinitely divisible distributions series representations shot noise random variables

Citation

Rosinski, Jan. On Series Representations of Infinitely Divisible Random Vectors. Ann. Probab. 18 (1990), no. 1, 405--430. doi:10.1214/aop/1176990956. https://projecteuclid.org/euclid.aop/1176990956


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