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April, 1975 A New Decomposition of Infinitely Divisible Distributions
D. N. Shanbhag, J. Gani
Ann. Probab. 3(2): 338-345 (April, 1975). DOI: 10.1214/aop/1176996404

Abstract

In this paper, it is shown that a random variable $Z$ having an infinitely divisible distribution with a finite left extremity can be decomposed in distribution as the sum of two random variables such that, given one, the other has an infinitely divisible distribution of prescribed type. Some extensions of this result when the left extremity is infinite are also given, and a new decomposition of a normal variable is exhibited.

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D. N. Shanbhag. J. Gani. "A New Decomposition of Infinitely Divisible Distributions." Ann. Probab. 3 (2) 338 - 345, April, 1975. https://doi.org/10.1214/aop/1176996404

Information

Published: April, 1975
First available in Project Euclid: 19 April 2007

zbMATH: 0313.60013
MathSciNet: MR370690
Digital Object Identifier: 10.1214/aop/1176996404

Subjects:
Primary: 60E05

Keywords: characteristic functions , conditional probability distributions , Infinitely divisible distributions , left extremity of distributions

Rights: Copyright © 1975 Institute of Mathematical Statistics

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Vol.3 • No. 2 • April, 1975
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