A general law of precise asymptotics for products of sums under dependence |
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| Authors: | Yong Zhang Xiao Yun Yang Zhi Shan Dong |
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| Institution: | 1. College of Mathematics, Jilin University, Changchun, 130012, P. R. China
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| Abstract: | Let ⨑ub;X
n
, n ≥ 1⫂ub; be a strictly stationary LNQD (LPQD) sequence of positive random variables with EX
1 = μ > 0, and VarX
1 = σ
2 < ∞. Denote by S
n
= Σ
i=1
n
X
i
and γ = σ/μ the coefficients of variation. In this paper, under some suitable conditions, we show that a general law of precise asymptotics
for products of sums holds. It can describe the relations among the boundary function, weighted function, convergence rate
and limit value in the study of complete convergence. |
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| Keywords: | general law precise asymptotics products of sums NA （PA） LNQD （LPQD） |
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