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The law of the iterated logarithm for certain power series and generalized Nörlund methods
Published online by Cambridge University Press: 24 October 2008
Abstract
Let (pn) be a sequence of real numbers with pn ~ R(n), R(.) a regulary varying function with index greater than −1/2. We prove the Hartman–Wintner law of the iterated logarithm for the corresponding (Jp) power series transform and generalized Nörlund transforms (Nβp) of sequences (Xn) of i.i.d. random variables with mean-zero and variance 1. We also identify the cluster sets.
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- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 120 , Issue 4 , November 1996 , pp. 735 - 753
- Copyright
- Copyright © Cambridge Philosophical Society 1996
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