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October, 1976 A Strong Convergence Theorem for Banach Space Valued Random Variables
J. Kuelbs
Ann. Probab. 4(5): 744-771 (October, 1976). DOI: 10.1214/aop/1176995982

Abstract

We prove a strong convergence theorem for Banach space valued random variables. One corollary of this result establishes necessary and sufficient conditions for the law of the iterated logarithm (LIL) in the Banach space setting. We also prove an exact generalization of the Hartman-Wintner law of the iterated logarithm provided the random variables involved take values in a real separable Hilbert space or some other Banach space with smooth norm.

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J. Kuelbs. "A Strong Convergence Theorem for Banach Space Valued Random Variables." Ann. Probab. 4 (5) 744 - 771, October, 1976. https://doi.org/10.1214/aop/1176995982

Information

Published: October, 1976
First available in Project Euclid: 19 April 2007

zbMATH: 0365.60034
MathSciNet: MR420771
Digital Object Identifier: 10.1214/aop/1176995982

Subjects:
Primary: 60B05
Secondary: 28A40, 60B10, 60F10

Rights: Copyright © 1976 Institute of Mathematical Statistics

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Vol.4 • No. 5 • October, 1976
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