What question did this study set out to answer?

The aim is to establish logarithmic asymptotic behaviors for the tail probabilities of sums of m-dependent random variables with super-heavy tails.

June 23, 2026

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

DLDawei LuNational University of Defense Technology YWYue WangUniversity of Stuttgart

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.

Abstract

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.

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Cite This Study

Lu et al. (Sun,) studied this question.

synapsesocial.com/papers/6a3a21f3111626ef22ab6af4 https://doi.org/https://doi.org/10.1080/03610926.2026.2671310

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