Large deviations for dependent heavy tailed random variables

Let {Xn, n ≥ 1} be a stationary sequence of random variables with heavy tails. In this paper, we study the logarithmic asymptotic behaviors for the distributions of the partial sums \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${S_n} = \sum\nolimits_{i = 1}^n {{X_i}} $$\end{document} under the assumption that {Xn, n ≥ 1} is a sequence of dependent random variables. Our main interest is in the crude estimates P(|Sn| > nx) ≈ n−ax+1 for appropriate values x where a is a specific parameter. Some results in this paper extend the works of Hu and Nyrhinen (2004).