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Invariance principles for logarithmic averages

Published online by Cambridge University Press:  24 October 2008

Miklós Csörgő  and
Lajos Horváth
Miklós Csörgő
Affiliation:
Department of Mathematics and Statistics, Carleton University, Ottawa, Ontario K1S 5B6, Canada
Lajos Horváth
Affiliation:
Department of Mathematics, University of Utah, Salt Lake City, Utah 84112, U.S.A.
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Abstract

We obtain weak and strong Gaussian approximations for logarithmic averages of indicators of normalized partial sums. The proofs are based on invariance principles for integrals of an Ornstein–Uhlenbeck process and on strong approximations of normalized partial sums by Orstein–Uhlenbeck processes.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 112 , Issue 1 , July 1992 , pp. 195 - 205
Copyright
Copyright © Cambridge Philosophical Society 1992

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