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February, 1983 Small Deviations in the Functional Central Limit Theorem with Applications to Functional Laws of the Iterated Logarithm
Alejandro de Acosta
Ann. Probab. 11(1): 78-101 (February, 1983). DOI: 10.1214/aop/1176993661

Abstract

We prove a small deviation theorem of a new form for the functional central limit theorem for partial sums of independent, identically distributed finite-dimensional random vectors. The result is applied to obtain a functional form of the Chung-Jain-Pruitt law of the iterated logarithm which is also a strong speed of convergence theorem refining Strassen's invariance principle.

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Alejandro de Acosta. "Small Deviations in the Functional Central Limit Theorem with Applications to Functional Laws of the Iterated Logarithm." Ann. Probab. 11 (1) 78 - 101, February, 1983. https://doi.org/10.1214/aop/1176993661

Information

Published: February, 1983
First available in Project Euclid: 19 April 2007

zbMATH: 0504.60033
MathSciNet: MR682802
Digital Object Identifier: 10.1214/aop/1176993661

Subjects:
Primary: 60F15

Keywords: other law of the iterated logarithm , Small deviations , Strassen's invariance principle

Rights: Copyright © 1983 Institute of Mathematical Statistics

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Vol.11 • No. 1 • February, 1983
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