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OL distributions on Euclidean spaces. (English) Zbl 0531.60015

A distribution function F(x) is said to be an OL distribution function or Lévy distribution function if there exists a sequence of independent random variables \(\underset \tilde{} X_ 1,\underset \tilde{} X_ 2,..\). such that for suitable linear operators \(A_ n\) and vectors \(\underset \tilde{} b_ n\) the distribution functions of the random variables \(A_ n(\underset \tilde{} X_ 1+...+\underset \tilde{} X_ n)-\underset \tilde{} b_ n\) converge completely to \(F(\underset \tilde{} x)\) and in addition the random variables \(A_ n\underset \tilde{} X_ j\) (1\(\leq j\leq n)\) form an infinitesimal system. In this paper the author gives a survey of work that has been done concerning OL distribution on Euclidean spaces.
Reviewer: S.J.Wolfe

MSC:

60E05 Probability distributions: general theory
60F05 Central limit and other weak theorems
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