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

We prove a deviation bound for the maximum of partial sums of functions of [Formula: see text]-dependent sequences as defined in [2]. As a consequence, we extend the Rosenthal inequality of Rio [16] for [Formula: see text]-mixing sequences in the sense of Rosenblatt [18] to the larger class of [Formula: see text]-dependent sequences. Starting from the deviation inequality, we obtain upper bounds for large deviations and Hölderian invariance principle for the Donsker line. We illustrate our results through the example of intermittent maps of the interval, which are not [Formula: see text]-mixing in the sense of Rosenblatt.

Complete Moment Convergence and Mean Convergence for Arrays of Rowwise Extended Negatively Dependent Random Variables

The authors first present a Rosenthal inequality for sequence of extended negatively dependent (END) random variables. By means of the Rosenthal inequality, the authors obtain some complete moment convergence and mean convergence results for arrays of rowwise END random variables. The results in this paper extend and improve the corresponding theorems by Hu and Taylor (1997).