An alternative to the coupling of Berkes-Liu-Wu for strong approximations

In this paper we propose an alternative to the coupling of Berkes, Liu and Wu [1] to obtain strong approximations for partial sums of dependent sequences. The main tool is a new Rosenthal type inequality expressed in terms of the coupling coefficients. These coefficients are well suited to some classes of Markov chains or dynamical systems, but they also give new results for smooth functions of linear processes.