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June, 1974 Berry-Esseen Estimates in Hilbert Space and an Application to the Law of the Iterated Logarithm
J. Kuelbs, T. Kurtz
Ann. Probab. 2(3): 387-407 (June, 1974). DOI: 10.1214/aop/1176996655

Abstract

We establish Berry-Esseen type estimates for random variables with values in a real separable Hilbert space $H$. These estimates are then used to prove the law of the iterated logarithm for sequences of $H$-valued random variables and also to prove a functional form of the law of the iterated logarithm for $H$-valued partial sums as given by Strassen. We also prove a $\log \log$ result for $H$-valued symmetric stable random variables.

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J. Kuelbs. T. Kurtz. "Berry-Esseen Estimates in Hilbert Space and an Application to the Law of the Iterated Logarithm." Ann. Probab. 2 (3) 387 - 407, June, 1974. https://doi.org/10.1214/aop/1176996655

Information

Published: June, 1974
First available in Project Euclid: 19 April 2007

zbMATH: 0298.60017
MathSciNet: MR362427
Digital Object Identifier: 10.1214/aop/1176996655

Keywords: 2846 , 6008 , 6030 , Abstract Wiener spaces , Berry-Esseen estimates , Brownian motion , Gaussian measures , Gaussian measures norm , measurable norm , Strassen's law of the iterated logarithm

Rights: Copyright © 1974 Institute of Mathematical Statistics

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Vol.2 • No. 3 • June, 1974
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