A new factorization property of the selfdecomposable probability measures

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

2002-05-30

arxiv.org/abs/math/0205316v3

Annals of Probability 2004, Vol. 32, No. 2, 1356-1369

Mathematics

Probability

Published at http://dx.doi.org/10.1214/009117904000000225 in the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

10.1214/009117904000000225

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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