- Volume 12, Number 1 (2006), 1-33.
Some classes of multivariate infinitely divisible distributions admitting stochastic integral representations
The class of distributions on generated by convolutions of Γ-distributions and the class generated by convolutions of mixtures of exponential distributions are generalized to higher dimensions and denoted by and . From the Lévy process on with distribution μ at t=1, Υ(μ) is defined as the distribution of the stochastic integral . This mapping is a generalization of the mapping Υ introduced by Barndorff-Nielsen and Thorbjørnsen in one dimension. It is proved that and , where and are the classes of infinitely divisible distributions and of self-decomposable distributions on , respectively. The relations with the mapping Φ from μ to the distribution at each time of the stationary process of Ornstein-Uhlenbeck type with background driving Lévy process are studied. Developments of these results in the context of the nested sequence , , are presented. Other applications and examples are given.
Bernoulli, Volume 12, Number 1 (2006), 1-33.
First available in Project Euclid: 28 February 2006
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Barndorff-Nielsen, Ole E.; Maejima, Makoto; Sato, Ken-Iti. Some classes of multivariate infinitely divisible distributions admitting stochastic integral representations. Bernoulli 12 (2006), no. 1, 1--33. https://projecteuclid.org/euclid.bj/1141136646