Limit Theorems for Sums of Independent Variables Taking into Account Large Deviations. III

Conditions are found which are necessary for uniform normal convergence in the zones $[0,n^\alpha \rho (n)],[ - n^\alpha \rho (n)]$ for values of $\alpha \in [\tfrac{1}{6},\tfrac{1}{2}]$, and sufficientin the zones $[0,{n^\alpha } /{\rho } (n)],[{ - n^\alpha } /{\rho } (n),0]$. The method is a combi...

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Bibliographic Details
Published in:Theory of probability and its applications 1962-04, Vol.7 (2), p.115-129
Main Author: Linnik, Yu. V.
Format: Article
Language:English
Subjects:
Independent variables
Random variables
Theorems
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Summary:Conditions are found which are necessary for uniform normal convergence in the zones $[0,n^\alpha \rho (n)],[ - n^\alpha \rho (n)]$ for values of $\alpha \in [\tfrac{1}{6},\tfrac{1}{2}]$, and sufficientin the zones $[0,{n^\alpha } /{\rho } (n)],[{ - n^\alpha } /{\rho } (n),0]$. The method is a combination of H. Cramer's method and of the arguments of Part I of this paper.
ISSN:0040-585X
1095-7219
DOI:10.1137/1107012