The Annals of Probability
- Ann. Probab.
- Volume 17, Number 1 (1989), 333-352.
Stability Results and Strong Invariance Principles for Partial Sums of Banach Space Valued Random Variables
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.
Ann. Probab., Volume 17, Number 1 (1989), 333-352.
First available in Project Euclid: 19 April 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60F17: Functional limit theorems; invariance principles
Secondary: 60F15: Strong theorems
Einmahl, Uwe. Stability Results and Strong Invariance Principles for Partial Sums of Banach Space Valued Random Variables. Ann. Probab. 17 (1989), no. 1, 333--352. doi:10.1214/aop/1176991512. https://projecteuclid.org/euclid.aop/1176991512