A deviation bound for $\alpha$-dependent sequences with applications to intermittent maps
Probability
2016-01-22 v1
Abstract
We prove a deviation bound for the maximum of partial sums of functions of -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 -mixing sequences in the sense of Rosenblatt (1956) to the larger class of -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 -mixing in the sense of Rosenblatt.
Cite
@article{arxiv.1601.05567,
title = {A deviation bound for $\alpha$-dependent sequences with applications to intermittent maps},
author = {J Dedecker and Florence Merlevède},
journal= {arXiv preprint arXiv:1601.05567},
year = {2016}
}