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Some Optimal Conditions for the ASCLT

Author

Listed:
  • István Berkes

    (A. Rényi Institute of Mathematics)

  • Siegfried Hörmann

    (Graz University of Technology)

Abstract

Let $$X_{1},X_{2},\ldots $$ X 1 , X 2 , … be independent random variables with $${E}X_{k}=0$$ E X k = 0 and $$\sigma _{k}^{\,2}:={E}X_{k}^2

Suggested Citation

  • István Berkes & Siegfried Hörmann, 2024. "Some Optimal Conditions for the ASCLT," Journal of Theoretical Probability, Springer, vol. 37(1), pages 209-227, March.
    • Handle: RePEc:spr:jotpro:v:37:y:2024:i:1:d:10.1007_s10959-023-01245-w
    DOI: 10.1007/s10959-023-01245-w
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    References listed on IDEAS

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    1. Berkes, István & Csáki, Endre & Horváth, Lajos, 1998. "Almost sure central limit theorems under minimal conditions," Statistics & Probability Letters, Elsevier, vol. 37(1), pages 67-76, January.
    2. 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.
    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.
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