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January 1997 Nested classes of $C$-decomposable laws
John Bunge
Ann. Probab. 25(1): 215-229 (January 1997). DOI: 10.1214/aop/1024404286


A random variable $X$ is C-decomposable if $X =_D cX + Y_c$ for all $c$ in $C$, where $_c$ is a random variable independent of $X$ and $C$ is a closed multiplicative subsemigroup of [0, 1]. $X$ is self-decomposable if $C = [0, 1]$ . Extending an idea of Urbanik in the self-decomposable case, we define a decreasing sequence of subclasses of the class of $C$-decomposable laws, for any $C$. We give a structural representation for laws in these classes, and we show that laws in the limiting subclass are infinitely divisible. We also construct noninfinitely divisible examples, some of which are continuous singular.


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John Bunge. "Nested classes of $C$-decomposable laws." Ann. Probab. 25 (1) 215 - 229, January 1997.


Published: January 1997
First available in Project Euclid: 18 June 2002

zbMATH: 0873.60005
MathSciNet: MR1428507
Digital Object Identifier: 10.1214/aop/1024404286

Primary: 60E05
Secondary: 60F05

Keywords: Class $L$ distribution , Decomposability semigroup , infinite Bernoulli convolution , infinitely divisible measure , normed sum , self-decomposable measure

Rights: Copyright © 1997 Institute of Mathematical Statistics


Vol.25 • No. 1 • January 1997
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