The Annals of Probability
- Ann. Probab.
- Volume 25, Number 1 (1997), 215-229.
Nested classes of $C$-decomposable laws
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.
Ann. Probab., Volume 25, Number 1 (1997), 215-229.
First available in Project Euclid: 18 June 2002
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Bunge, John. Nested classes of $C$-decomposable laws. Ann. Probab. 25 (1997), no. 1, 215--229. doi:10.1214/aop/1024404286. https://projecteuclid.org/euclid.aop/1024404286