Precise asymptotics in some strong limit theorems for multidimensionally indexed random variables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 in some strong limit theorems for multidimensionally indexed random variables

Authors:	Allan Gut Aurel Sptaru

Affiliation:	^a Department of Mathematics, Uppsala University, P.O. Box 480, SE-75106, Uppsala, Sweden;^b Centre of Mathematical Statistics, Romanian Academy, Calea 13 Septembrie No. 13, Ro-761 00, Bucharest 5, Romania

Abstract:	Consider Z₊^d (d2)—the positive d-dimensional lattice points with partial ordering , let {X_k,kZ₊^d} be i.i.d. random variables with mean 0, and set S_n=∑_knX_k, nZ₊^d. We establish precise asymptotics for ∑_n\|n\|^r/p−2P(\|S_n\|\|n\|^1/p), and for Full-size image , (0δ1) as 0, and for Full-size image as .

Keywords:	Multidimensional indices Tail probabilities of sums of i.i.d. random variables Stable distributions Domain of attraction Strong law Law of the iterated logarithm
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