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

Abstract

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