Precise large deviations for widely orthant dependent random variables with different distributions

Abstract Let X i, i ≥ 1 $X_{i}, i\geq1$ be a sequence of random variables with different distributions F i, i ≥ 1 $F_{i}, i\geq1$. The partial sums are denoted by S n = ∑ i = 1 n X i $S_{n}=\sum_{i=1}^{n} X_{i}$, n ≥ 1 $n\geq1$. This paper mainly investigates the precise large deviations of S n, n ≥ 1 $S_{n}, n\geq1$, for the widely orthant dependent random variables X i, i ≥ 1 $X_{i}, i\geq1$. Under some mild conditions, the lower and upper bounds of the precise large deviations of the partial sums S n $S_{n}$, n ≥ 1 $n\geq1$, are presented.

Abstract licence: CC BY-NC-ND

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