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Large Deviations for the Maximum of the Absolute Value of Partial Sums of Random Variable Sequences

Author

Listed:
  • Xia Wang

    (Faculty of Science, College of Statistics and Date Science, Beijing University of Technology, Beijing 100124, China)

  • Miaomiao Zhang

    (Faculty of Science, College of Statistics and Date Science, Beijing University of Technology, Beijing 100124, China)

Abstract

Let { ξ i : i ≥ 1 } be a sequence of independent, identically distributed (i.i.d. for short) centered random variables. Let S n = ξ 1 + ⋯ + ξ n denote the partial sums of { ξ i } . We show that sequence { 1 n max 1 ≤ k ≤ n | S k | : n ≥ 1 } satisfies the large deviation principle (LDP, for short) with a good rate function under the assumption that P ( ξ 1 ≥ x ) and P ( ξ 1 ≤ − x ) have the same exponential decrease.

Suggested Citation

  • Xia Wang & Miaomiao Zhang, 2022. "Large Deviations for the Maximum of the Absolute Value of Partial Sums of Random Variable Sequences," Mathematics, MDPI, vol. 10(5), pages 1-11, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:5:p:758-:d:759976
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    References listed on IDEAS

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    1. Li, Yulin, 2003. "A martingale inequality and large deviations," Statistics & Probability Letters, Elsevier, vol. 62(3), pages 317-321, April.
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    Cited by:

    1. Alexander N. Tikhomirov & Vladimir V. Ulyanov, 2023. "On the Special Issue “Limit Theorems of Probability Theory”," Mathematics, MDPI, vol. 11(17), pages 1-4, August.

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