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Refinement of Convergence Rates for Tail Probabilities

Authors:	Deli?Li author-information" > author-information__contact u-icon-before" > mailto:lideli@giant.lakeheadu.ca" title=" lideli@giant.lakeheadu.ca" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author,Aurel?Sp?taru

Affiliation:	(1) Department of Mathematical Sciences, Lakehead University, Thunder Bay, Ontario, P7B 5E1, Canada;(2) Institute of Mathematical Statistics and Applied Mathematics, Romanian Academy, Calea 13 Septembrie No 13, 761 00 Bucharest 5, Romania

Abstract:	Let X₁, X₂,... be, i.i.d. random variables, and put $S_{n}=X_{1}+cdots+X_{n}$ . We find necessary and sufficient moment conditions for $int_{varepsilon }^{infty }f(x^{q})dx < infty , varepsilon >delta$ , where δ≥ 0 and q>0, and $f(x)=sum_{n}a_{n}P(leftvert S_{n}rightvert >xb_{n})$ with a_n>0 and b_n is either $n^{1/p},,0<p<2,,sqrt{n,log,n}$ or The series f(x) we deal with are classical series studied by Hsu and Robbins, Erdős, Spitzer, Baum and Katz, Davis, Lai, Gut, etc

Keywords:	Complete convergence Hoffmann– J?rgensen inequality large deviation moderate deviation law of large numbers law of the iterated logarithm
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