Large deviations for dependent heavy tailed random variables

Let {Xn,n≥1}{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 Sn=∑i=1nXi under the assumption that {Xn,n≥1}{Xn,n≥1} is a sequence of dependent random variables. Our main interest is in the crude estimates P(|Sn|>nx)≈n−αx+1P(|Sn|>nx)≈n−αx+1 for appropriate values xx where αα is a specific parameter. Some results in this paper extend the works of Hu and Nyrhinen (2004).