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 L^f denote the set of all these distributions. The algebraic structure and various characterizations of L^f are studied. Some examples are discussed, the most interesting one being given by the Levy stochastic area integral. A nested family of subclasses L^f_n, n\ge 0, (or a filtration) of the class L^f is given.
Cite
@article{arxiv.math/0205316,
title = {A new factorization property of the selfdecomposable probability measures},
author = {Aleksander M. Iksanov and Zbigniew J. Jurek and Bertram M. Schreiber},
journal= {arXiv preprint arXiv:math/0205316},
year = {2007}
}
Comments
Published at http://dx.doi.org/10.1214/009117904000000225 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)