Open Access
November 2007 Strong invariance principles for dependent random variables
Wei Biao Wu
Ann. Probab. 35(6): 2294-2320 (November 2007). DOI: 10.1214/009117907000000060


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.


Published: November 2007
First available in Project Euclid: 8 October 2007

zbMATH: 1166.60307
MathSciNet: MR2353389
Digital Object Identifier: 10.1214/009117907000000060

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

Rights: Copyright © 2007 Institute of Mathematical Statistics

Vol.35 • No. 6 • November 2007
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