Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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LARGE DEVIATIONS FOR A SUPER-HEAVY TAILED 𝛽-MIXING SEQUENCE

  • Yu Miao (College of Mathematics and Information Science Henan Normal University) ;
  • Qing Yin (College of Mathematics and Information Science Henan Normal University)
  • Received : 2022.11.18
  • Accepted : 2024.04.25
  • Published : 2024.09.01
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Abstract

Let {X, Xn; n ≥ 1} be a 𝛽-mixing sequence of identical nonnegative random variables with super-heavy tailed distributions and Sn = X1 + X2 + · · · + Xn. For 𝜀 > 0, b > 1 and appropriate values of x, we obtain the logarithmic asymptotics behaviors for the tail probabilities ℙ(Sn > e𝜀nx) and P(Sn > e𝜀bn). Moreover, our results are applied to the log-Pareto distribution and the distribution for the super-Petersburg game.

Keywords

Acknowledgement

The authors would like to express their sincere gratitude to the anonymous referees and editor for their helpful comments which led to an improved presentation of this paper.

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