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