## The Annals of Probability

### Strong invariance principles for dependent random variables

Wei Biao Wu

#### Abstract

We establish strong invariance principles for sums of stationary and ergodic processes with nearly optimal bounds. Applications to linear and some nonlinear processes are discussed. Strong laws of large numbers and laws of the iterated logarithm are also obtained under easily verifiable conditions.

#### Article information

Source
Ann. Probab. Volume 35, Number 6 (2007), 2294-2320.

Dates
First available in Project Euclid: 8 October 2007

http://projecteuclid.org/euclid.aop/1191860422

Digital Object Identifier
doi:10.1214/009117907000000060

Mathematical Reviews number (MathSciNet)
MR2353389

Zentralblatt MATH identifier
05211873

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 60F17: Functional limit theorems; invariance principles

#### Citation

Wu, Wei Biao. Strong invariance principles for dependent random variables. Ann. Probab. 35 (2007), no. 6, 2294--2320. doi:10.1214/009117907000000060. http://projecteuclid.org/euclid.aop/1191860422.

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