Semi-selfdecomposable distributions and a new class of limit theorems |
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Authors: | Makoto Maejima Yoshihiro Naito |
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Institution: | (1) Department of Mathematics, Keio University, Hiyoshi 3-14-1, Kohoku-ku, Yokohama 223, Japan e-mail: maejima@math.keio.ac.jp, JP |
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Abstract: | Self-decomposable distributions are given as limits of normalized sums of independent random variables. We define semi-selfdecomposable
distributions as limits of subsequences of normalized sums. More generally, we introduce a way of making a new class of limiting
distributions derived from a class of distributions by taking the limits through subsequences of normalized sums, and define
the class of semi-selfdecomposable distributions and a decreasing sequence of subclasses of it. We give two kinds of necessary
and sufficient conditions for distributions belonging to those classes, one is in terms of the decomposability of random variables
and another is in terms of Lévy measures.
Received: 1 May 1997 / Revised version: 5 February 1998 |
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Keywords: | Mathematics Subject Classification (1991): 60E07 (primary) 60E10 60F05 |
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