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A general large deviation result for partial sums of i.i.d. super-heavy tailed random variables

Author

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  • Li, Deli
  • Miao, Yu
  • Stoica, George

Abstract

In this paper, a general large deviation result for partial sums of independent and identically distributed random variables with super-heavy tailed distribution is established. Our main result extends in particular the results of Stoica (2008) and Nakata (2022). The symmetrization technique, one of Lévy’s inequalities, and two preliminary results on slowly and regularly varying functions are paramount in the proof of our main result.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:stapro:v:184:y:2022:i:c:s0167715222000050
    DOI: 10.1016/j.spl.2022.109371
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    References listed on IDEAS

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    1. Gantert, Nina, 2000. "A note on logarithmic tail asymptotics and mixing," Statistics & Probability Letters, Elsevier, vol. 49(2), pages 113-118, August.
    2. Nakata, Toshio, 2022. "Large deviations for super-heavy tailed random walks," Statistics & Probability Letters, Elsevier, vol. 180(C).
    3. Y. Hu & H. Nyrhinen, 2004. "Large Deviations View Points for Heavy-Tailed Random Walks," Journal of Theoretical Probability, Springer, vol. 17(3), pages 761-768, July.
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