• 제목/요약/키워드: ${\beta}$-mixing sequence

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LARGE DEVIATIONS FOR A SUPER-HEAVY TAILED 𝛽-MIXING SEQUENCE

  • Yu Miao;Qing Yin
    • 대한수학회지
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    • 제61권5호
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    • pp.853-874
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    • 2024
  • 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.