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A Precise Asymptotic Behaviour of the Large Deviation Probabilities for Weighted Sums
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Applied Mathematics·Volume 02 (2011)·Pages 1175–1181·Published 29 September 2011·DOI10.4236/am.2011.29163
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Abstract
Let {X<sub>n</sub>, n ≥ 1} be a sequence of independent and identically distributed positive valued random variables with a common distribution function F. When F belongs to the domain of partial attraction of a semi stable law with index α, 0 < α < 1, an asymptotic behavior of the large deviation probabilities with respect to properly normalized weighted sums have been studied and in support of this we obtained Chover’s form of law of iterated logarithm.
KeywordsLarge DeviationsLaw of Iterated LogarithmSemi-Stable LawDomain of Partial AttractionWeighted Sums
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