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Berry-Esseen Estimates in Hilbert Space and an Application to the Law of the Iterated Logarithm

J. Kuelbs and T. Kurtz
The Annals of Probability
Vol. 2, No. 3 (Jun., 1974), pp. 387-407
Stable URL: http://www.jstor.org/stable/2959173
Page Count: 21
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Berry-Esseen Estimates in Hilbert Space and an Application to the Law of the Iterated Logarithm
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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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