A deviation bound for $α$-dependent sequences with applications to intermittent maps

Abstract

We prove a deviation bound for the maximum of partial sums of functions of $α$-dependent sequences as defined in Dedecker, Gou{ë}zel and Merlev{è}de (2010). As a consequence, we extend the Rosenthal inequality of Rio (2000) for $α$-mixing sequences in the sense of Rosenblatt (1956) to the larger class of $α$-dependent sequences. Starting from the deviation inequality, we obtain upper bounds for large deviations and an H{ö}lderian invariance principle for the Donsker line. We illustrate our results through the example of intermittent maps of the interval, which are not $α$-mixing in the sense of Rosenblatt.