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A local limit theorem for attractions under a stable law
Published online by Cambridge University Press: 24 October 2008
Abstract
Let {Xn} be a sequence of independent random variables each having a common d.f. V1. Suppose that V1 belongs to the domain of normal attraction of a stable d.f. V0 of index α 0 ≤ α ≤ 2. Here we prove that, if the c.f. of X1 is absolutely integrable in rth power for some integer r > 1, then for all large n the d.f. of the normalized sum Zn of X1, X2, …, Xn is absolutely continuous with a p.d.f. vn such that
as n → ∞, where v0 is the p.d.f. of Vo.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 87 , Issue 1 , January 1980 , pp. 179 - 187
- Copyright
- Copyright © Cambridge Philosophical Society 1980
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