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

Makoto Maejima, Ken-iti Sato

Published 2007-12-03Version 1

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.