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Almost Sure Convergence for the Maximum and Minimum of Normal Vector Sequences

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  • Zhicheng Chen

    (State Key Laboratory of Mechanics and Control of Mechanical Structures, Institute of Nano Science and Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
    Department of Mathematics, Henan Institute of Science and Technology, Xinxiang 453003, China)

  • Hongyun Zhang

    (Department of Mathematics, Henan Institute of Science and Technology, Xinxiang 453003, China)

  • Xinsheng Liu

    (State Key Laboratory of Mechanics and Control of Mechanical Structures, Institute of Nano Science and Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China)

Abstract

In this paper, we prove the almost sure convergences for the maximum and minimum of nonstationary and stationary standardized normal vector sequences under some suitable conditions.

Suggested Citation

  • Zhicheng Chen & Hongyun Zhang & Xinsheng Liu, 2020. "Almost Sure Convergence for the Maximum and Minimum of Normal Vector Sequences," Mathematics, MDPI, vol. 8(4), pages 1-11, April.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:618-:d:346809
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    References listed on IDEAS

    as
    1. Fahrner, I. & Stadtmüller, U., 1998. "On almost sure max-limit theorems," Statistics & Probability Letters, Elsevier, vol. 37(3), pages 229-236, March.
    2. Csáki, Endre & Gonchigdanzan, Khurelbaatar, 2002. "Almost sure limit theorems for the maximum of stationary Gaussian sequences," Statistics & Probability Letters, Elsevier, vol. 58(2), pages 195-203, June.
    3. Berkes, István & Csáki, Endre, 2001. "A universal result in almost sure central limit theory," Stochastic Processes and their Applications, Elsevier, vol. 94(1), pages 105-134, July.
    4. Gonchigdanzan, Khurelbaatar, 2008. "An almost sure limit theorem for the product of partial sums with stable distribution," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3170-3175, December.
    5. Chen, Shouquan & Lin, Zhengyan, 2006. "Almost sure max-limits for nonstationary Gaussian sequence," Statistics & Probability Letters, Elsevier, vol. 76(11), pages 1175-1184, June.
    6. Ibragimov, Ildar & Lifshits, Mikhail, 1998. "On the convergence of generalized moments in almost sure central limit theorem," Statistics & Probability Letters, Elsevier, vol. 40(4), pages 343-351, November.
    Full references (including those not matched with items on IDEAS)

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