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

Key Points

• The aim is to establish logarithmic asymptotic behaviors for the tail probabilities of sums of m-dependent random variables with super-heavy tails.
• Analyzed a stationary sequence of m-dependent and identically distributed random variables.
• Derived the tail probabilities P(|Sn|>eεnx) and P(|Sn|>eεbn) for ε>0 and b>1.
• Applied results to a transformed log-Pareto distribution.
• Obtained specific logarithmic asymptotic expressions for the tail probabilities.
• Demonstrated that super-heavy tails significantly influence the behavior of the sums.
• Provided applications to the log-Pareto distribution indicating broad relevance.