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Some Results on Small-Deviation Probability Convergence Rates for Sums of Independent Random Variables

Published online by Cambridge University Press:  20 November 2018

C. C. Heyde
C. C. Heyde*
Affiliation:
Michigan State University
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Let ﹛Xj,j = 1, 2, 3, …﹜ be a sequence of independent, non-degenerate random variables and write

Under quite a diverse variety of conditions we may obtain

as n → ∞ for all x, — ∞ < x < ∞, and some real p ⩾ 0. For example, suppose the ﹛Xj﹜ happen to be distributed identically and belong to the domain of normal attraction of a symmetric stable law with characteristic exponent α, 0 < α ⩽ < 2, α ≠ 1.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 656 - 665
Copyright
Copyright © Canadian Mathematical Society 1966

References

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