The limits of nested subclasses of several classes of infinitely divisible distributions are identical with the closure of the class of stable distributions

Details The limits of nested subclasses of several classes of infinitely divisible distributions are identical with the closure of the class of stable distributions The limits of nested subclasses of several classes of infinitely divisible distributions are identical with the closure of the class of stable distributions

2007-12-03

arxiv.org/abs/0712.0206v1

Mathematics

Probability

22 pages

Scientific paper

It is shown that the limits of the nested subclasses of five classes of infinitely divisible distributions on $R^d$, which are the Jurek class, the Goldie-Steutel-Bondesson class, the class of selfdecomposable distributions, the Thorin class and the class of generalized type $G$ distributions, are identical with the closure of the class of stable distributions. More general results are also given.

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