Precise asymptotics for a series of T. L. Lai期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Precise asymptotics for a series of T. L. Lai

Authors:	Aurel Spataru

Affiliation:	Institute of Mathematical Statistics and Applied Mathematics, Romanian Academy, Calea 13 Septembrie.13, 76100 Bucharest, Romania

Abstract:	Let $X,~X_{1},,X_{2},...$ be i.i.d. random variables with , and set $S_{n}=X_{1}+...+X_{n}$ . We prove that, for $begin{displaymath}lim_{varepsilon searrow sigma sqrt{2p-2}}sqrt{varepsil... ...geq varepsilon sqrt{nlog n} )=sigma sqrt{frac{2}{p-1}}, end{displaymath}$ under the assumption that $EX^{2}=sigma ^{2}$ and $E[leftvert Xrightvert ^{2p}(log ^{+}leftvert Xrightvert )^{-p}]<infty .$ Necessary and sufficient conditions for the convergence of the sum above were established by Lai (1974).

Keywords:	Tail probabilities of sums of i.i.d. random variables moderate deviations Lai law

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