2002/05/31 by Aleksander M. Iksanov, Zbigniew J. Jurek, Bertram M. Schreiber
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Probability and Risk Models #Random Matrices and Applications #Stochastic processes and financial applications #math.PR #msc:60B12 #msc:60E07 #msc:60G51 #msc:60H05.
paper · pdf · doi:10.1214/009117904000000225
published as Annals of Probability 2004, Vol. 32, No. 2, 1356-1369 · 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)
openalex publication_date 2004/04/01 · arxiv created 2005/03/30 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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, n≥0, (or a filtration) of the class Lf is given.