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January, 1989 Stability Results and Strong Invariance Principles for Partial Sums of Banach Space Valued Random Variables
Uwe Einmahl
Ann. Probab. 17(1): 333-352 (January, 1989). DOI: 10.1214/aop/1176991512

Abstract

A general stability theorem for $B$-valued random variables is obtained which refines a result of Kuelbs and Zinn. Our proof is based on two exponential inequalities for sums of independent $B$-valued r.v.'s essentially due to Yurinskii and appears particularly simple. We then use our theorem to prove strong invariance principles, LIL results and other related stability results for sums of i.i.d. $B$-valued r.v.'s in the domain of attraction of a Gaussian law. Most of these results seem to be still unknown for real-valued r.v.'s.

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Uwe Einmahl. "Stability Results and Strong Invariance Principles for Partial Sums of Banach Space Valued Random Variables." Ann. Probab. 17 (1) 333 - 352, January, 1989. https://doi.org/10.1214/aop/1176991512

Information

Published: January, 1989
First available in Project Euclid: 19 April 2007

zbMATH: 0669.60035
MathSciNet: MR972789
Digital Object Identifier: 10.1214/aop/1176991512

Subjects:
Primary: 60F17
Secondary: 60F15

Keywords: compact law of the iterated logarithm , Exponential inequalities , stability results , Strong invariance principles

Rights: Copyright © 1989 Institute of Mathematical Statistics

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Vol.17 • No. 1 • January, 1989
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