A method and device for precise large-scale angular measurements in precision manufacturing is described.
See, for example, Liu [4] obtained the precise large deviations for dependent random variables with heavy tails.
We study the precise large deviations for ({S_{n}, n geq0}) in (1.1).
This paper investigates the precise large deviations for these partial sums (S_{n}), (ngeq1).
Among them, Yang and Wang [32] consider the precise large deviations for extendedly negatively orthant dependent r.v.s, and Wang et al. [20] investigate the precise large deviations for WUOD and WLOD r.v.s.
The first one is an important precise large deviation for partial sums, which was originally due to Baltrūnas et al. [10] and modified by Daley et al. [16].
In this paper, we are interested in the precise large deviations for the randomly index sums (random sums) S N ( t ) under the assumption that the distribution B is heavy tailed.
The goal of this paper is studying the precise large deviations for the aggregate claims S_{n}=sum_{t=1}^{n} sum_{j=1}^{N_{t}}X_{t,j}, (1.1) where (N_{t}) is the number of claims in period t and ({X_{t,j}, j=1,2,ldots, t=1,2,ldots,n}) form an array of independent identically distributed (i.i.d).i.d
This paper investigates some precise large deviations for the random sums of the differences between two sequences of independent and identically distributed random variables, where the minuend random variables have subexponential tails, and the subtrahend random variables have finite second moments.
We remark that Baltrūnas et al. [7] obtained an important equivalently precise large deviations result for the random sums of nonnegative subexponential r.v.s.
Clearly, Lemma 3.1 and Theorem 1.1 lead to some precise large deviation results for the processes W n and W ( t ) in the CIRM.
