The Annals of Probability

Strong invariance principles for dependent random variables

Wei Biao Wu

Full-text: Open access

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

Permanent link to this document
https://projecteuclid.org/euclid.aop/1191860422

Digital Object Identifier
doi:10.1214/009117907000000060

Mathematical Reviews number (MathSciNet)
MR2353389

Zentralblatt MATH identifier
1166.60307

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

Keywords
Short- and long-range dependence strong convergence nonlinear time series martingale linear process law of the iterated logarithm strong invariance principle

Citation

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


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