The limits of nested subclasses of several classes of infinitely divisible distributions are identical with the closure of the class of stable distributions |
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| Authors: | Makoto Maejima Ken-iti Sato |
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| Institution: | 1. Department of Mathematics, Keio University, 3-14-1, Hiyoshi, Kohoku-ku, Yokohama, 223-8522, Japan
2. Hachiman-yama 1101-5-103, Tenpaku-ku, Nagoya, 468-0074, Japan
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| Abstract: | It is shown that the limits of the nested subclasses of five classes of infinitely divisible distributions on ${\mathbb{R}^{d}}$ , 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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