Strong invariance principles for dependent random variables

Wei Biao Wu

doi:10.1214/009117907000000060

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Home > Journals > Ann. Probab. > Volume 35 > Issue 6 > Article

November 2007 Strong invariance principles for dependent random variables

Wei Biao Wu

Ann. Probab. 35(6): 2294-2320 (November 2007). DOI: 10.1214/009117907000000060

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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.

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Wei Biao Wu. "Strong invariance principles for dependent random variables." Ann. Probab. 35 (6) 2294 - 2320, November 2007. https://doi.org/10.1214/009117907000000060

Information

Published: November 2007

First available in Project Euclid: 8 October 2007

zbMATH: 1166.60307

MathSciNet: MR2353389

Digital Object Identifier: 10.1214/009117907000000060

Subjects:

Primary: 60F05

Secondary: 60F17

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