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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

Rüdiger Kiesel
Rüdiger Kiesel
Affiliation:
Universität Ulm, Abteilung Stochastik, D-89069 Ulm, Germany e-mail: [email protected]
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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.

Type
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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