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Large Deviations View Points for Heavy-Tailed Random Walks

Author

Listed:
  • Y. Hu

    (Wuhan University)

  • H. Nyrhinen

    (University of Helsinki)

Abstract

Let X 1, X 2,... be a sequence of i.i.d. non-negative random variables with heavy tails. W e study logarithmic asymptotics for the distributions of the partial sums S n = X 1 + ··· + X n . Our main interest is in the crude estimates P(S n > n x ) ≈ n −αx + 1 for appropriate values of x where α is a specific parameter. The related conjecture proposed by Gantert (Stat. Probab. Lett. 49, 113–118) is investigated.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jotpro:v:17:y:2004:i:3:d:10.1023_b:jotp.0000040298.43712.e8
    DOI: 10.1023/B:JOTP.0000040298.43712.e8
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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).
    2. Harri Nyrhinen, 2009. "On Large Deviations of Multivariate Heavy-Tailed Random Walks," Journal of Theoretical Probability, Springer, vol. 22(1), pages 1-17, March.

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