A new factorization property of the selfdecomposable probability measures

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dc.creatorIksanov, Aleksander M.
dc.creatorJurek, Zbigniew J.
dc.creatorSchreiber, Bertram M.
dc.date2002-05-30
dc.date2005-03-30
dc.date.accessioned2026-07-07T04:48:48Z
dc.date.available2026-07-07T04:48:48Z
dc.descriptionWe 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.
dc.descriptionPublished 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)
dc.identifierhttps://arxiv.org/abs/math/0205316
dc.identifierhttp://arxiv.org/abs/math/0205316
dc.identifierAnnals of Probability 2004, Vol. 32, No. 2, 1356-1369
dc.identifierdoi:10.1214/009117904000000225
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/64187
dc.subjectProbability
dc.subject60E07, 60B12 (Primary) 60G51, 60H05. (Secondary)
dc.titleA new factorization property of the selfdecomposable probability measures
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