Large deviations for m -dependent super-heavy tailed random variables

Let {X,Xn,n≥1} be a stationary and symmetric sequence of m-dependent and identically distributed random variables with super-heavy tails and Sn=∑k=1nXk. In this paper, for ε>0, b>1 and appropriate values of x, we obtain the logarithmic asymptotic behaviors for the tail probabilities P(|Sn|>eεnx) and P(|Sn|>eεbn). Finally, we apply the result to a transformed distribution based on log-Pareto distribution.