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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Summability methods for independent identically distributed random variables
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by Tze Leung Lai PDF
Proc. Amer. Math. Soc. 45 (1974), 253-261 Request permission

Abstract:

In this paper, we present certain theorems concerning the Cesaro $(C,\alpha )$, Abel $(A)$, Euler $(E,q)$ and Borel $(B)$ summability of $\Sigma {Y_i}$, where ${Y_i} = {X_i} - {X_{i - 1}},{X_0} = 0$ and ${X_1},{X_2}, \cdots$ are i.i.d. random variables. While the Kolmogorov strong law of large numbers and the Hartman-Wintner law of the iterated logarithm are related to $(C,1)$ summability and involve the finiteness of, respectively, the first and second moments of ${X_1}$, their analogues for Euler and Borel summability involve different moment conditions, and the analogues for $(C,\alpha )$ and Abel summability remain essentially the same.
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 45 (1974), 253-261
  • MSC: Primary 60F15
  • DOI: https://doi.org/10.1090/S0002-9939-1974-0356194-4
  • MathSciNet review: 0356194