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

Let Xi, i >= 1 be a sequence of random variables with different distributions F-i, i >= 1. The partial sums are denoted by S-n = Sigma(n)(i=1) X-i, n >= 1. This paper mainly investigates the precise large deviations of S-n, n >= 1, for the widely orthant dependent random variables X-i, i >= 1. Under some mild conditions, the lower and upper bounds of the precise large deviations of the partial sums S-n, n >= 1, are presented.