We give rates of convergence in the strong invariance principle for stationary sequences satisfying some projective criteria. The conditions are expressed in terms of conditional expectations of partial sums of the initial sequence. Our results apply to a large variety of examples. We present some applications to a reversible Markov chain, to symmetric random walks on the circle, and to functions of dependent sequences.
"Rates of convergence in the strong invariance principle under projective criteria." Electron. J. Probab. 17 1 - 31, 2012. https://doi.org/10.1214/EJP.v17-1849