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Some Results on Small-Deviation Probability Convergence Rates for Sums of Independent Random Variables
Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 656-665

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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. 
Heyde, C. C. Some Results on Small-Deviation Probability Convergence Rates for Sums of Independent Random Variables. Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 656-665. doi: 10.4153/CJM-1966-066-x
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