Strong invariance principles for dependent random variables

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.

Published in at http://dx.doi.org/10.1214/009117907000000060 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (3)

• Martingale approximations for sums of stationary processes
• A new maximal inequality and invariance principle for stationary sequences
• On weighted U-statistics for stationary processes

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