## 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.## References

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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