## The Annals of Probability

### A new factorization property of the selfdecomposable probability measures

#### Abstract

We prove that the convolution of a selfdecomposable distribution with its background driving law is again selfdecomposable if and only if the background driving law is s-selfdecomposable. We will refer to this as the factorization property of a selfdecomposable distribution; let Lf denote the set of all these distributions. The algebraic structure and various characterizations of Lf are studied. Some examples are discussed, the most interesting one being given by the Lévy stochastic area integral. A nested family of subclasses Lfn, n0, (or a filtration) of the class Lf is given.

#### Article information

Source
Ann. Probab., Volume 32, Number 2 (2004), 1356-1369.

Dates
First available in Project Euclid: 18 May 2004

https://projecteuclid.org/euclid.aop/1084884853

Digital Object Identifier
doi:10.1214/009117904000000225

Mathematical Reviews number (MathSciNet)
MR2060300

Zentralblatt MATH identifier
1046.60002

#### Citation

Iksanov, Aleksander M.; Jurek, Zbigniew J.; Schreiber, Bertram M. A new factorization property of the selfdecomposable probability measures. Ann. Probab. 32 (2004), no. 2, 1356--1369. doi:10.1214/009117904000000225. https://projecteuclid.org/euclid.aop/1084884853

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