Abstract
Let X_{i}, igeq1 be a sequence of random variables with different distributions F_{i}, igeq1. The partial sums are denoted by S_{n}=sum_{i=1}^{n} X_{i}, ngeq1. This paper mainly investigates the precise large deviations of S_{n}, ngeq1, for the widely orthant dependent random variables X_{i}, igeq1. Under some mild conditions, the lower and upper bounds of the precise large deviations of the partial sums S_{n}, ngeq1, are presented.
Highlights
Let Xi (i ≥ 1) and X be real-valued random variables (r.v.s) with distributions Fi (i ≥ 1)and F and finite means μi (i ≥ 1) and μ, respectively
This paper mainly investigates the precise large deviations of Sn, n ≥ 1, for the widely orthant dependent random variables Xi, i ≥ 1
For the lower bound of the precise large deviations of the partial sums Sn, n ≥ 1, of the widely orthant dependent (WOD) r.v.s, when μi = 0, i ≥ 1, under Assumptions 1 and 3 and some other conditions, Theorem 2 of Wang et al [20] obtained a lower bound: for every fixed γ > 0, lim inf inf n→∞ x≥γ n
Summary
Let Xi (i ≥ 1) and X be real-valued random variables (r.v.s) with distributions Fi (i ≥ 1)and F and finite means μi (i ≥ 1) and μ, respectively. For the lower bound of the precise large deviations of the partial sums Sn, n ≥ 1, of the WOD r.v.s, when μi = 0, i ≥ 1, under Assumptions 1 and 3 and some other conditions, Theorem 2 of Wang et al [20] obtained a lower bound: for every fixed γ > 0, lim inf inf n→∞ x≥γ n
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