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Large deviations for super-heavy tailed random walks

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  • Nakata, Toshio

Abstract

In this article, we study large deviations for sums of independent and identically distributed random variables (random walks) with nonnegative super-heavy tailed distributions. While Hu and Nyrhinen (2004) gave results for heavy tailed distributions, our result is an improvement of one of theirs for super-heavy tailed ones. Moreover, we apply it to the log-Pareto distribution and the distribution for the super-Petersburg game.

Suggested Citation

  • Nakata, Toshio, 2022. "Large deviations for super-heavy tailed random walks," Statistics & Probability Letters, Elsevier, vol. 180(C).
    • Handle: RePEc:eee:stapro:v:180:y:2022:i:c:s0167715221002029
    DOI: 10.1016/j.spl.2021.109240
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    References listed on IDEAS

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    1. Nakata, Toshio, 2016. "Weak laws of large numbers for weighted independent random variables with infinite mean," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 124-129.
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    Cited by:

    1. Li, Deli & Miao, Yu & Stoica, George, 2022. "A general large deviation result for partial sums of i.i.d. super-heavy tailed random variables," Statistics & Probability Letters, Elsevier, vol. 184(C).

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