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

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