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arXiv math/02053162002-05math.PR

A new factorization property of the selfdecomposable probability measures

Aleksander M. Iksanov, Zbigniew J. Jurek, Bertram M. Schreiber

备注：: 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)
发表信息：: Annals of Probability 2004, Vol. 32, No. 2, 1356-1369
DOI：: 10.1214/009117904000000225

英文摘要：

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.

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