Asymptotics Lower Bounds Of Precise Large Deviations For Sums Of Nonnegative Dependent Random Variables

It is well known that deviation theory is one of the hot research issues in proba-bilistic theory, scholars concentrated on the issue for a long time, and many results in this field have been obtained. In this paper, based on the work of Konstantinides and Loukissas(2011), we study some asymptotic lower bounds of precise large deviations for non-random sums and random sums of nonnegative random variables (r.v.s) under some fairly weak conditions. The obtained results are used to derive asymptotic lower bounds of precise large deviations in a multi-risk model. All the results we established extend and improve the related existing results substantially.