Asymptotical Tail Behavior Of The Random Sums Of Dependent Random Variables

In this paper, we research the asymptotical tail behavior of the random sumsof dependent random variables. We note that many results on the random sums ofdependent random variables have been obtained based on restricting the distributionsto the subclass of subexponential distributions. Such as, Yu et al.(2014) require thedistributions F∈S. The results of this paper obtain the asymptotical tail behaviorof the random sums of dependent random variables under the assumption that thedistributions belong to the class of subexponential distributions.On the other hand, we also study the uniform asymptotic of the weighted sums ofdependent random variables. Most of the results about the uniform asymptotic of theweighted sums require that the distributions belong to the subclass of subexponentialdistributions. For example, Chen and Yuen (2009)!Liu et al.(2012)!Yu et al.(2014)obtained the asymptotic tail behavior of the weighted sums of dependent random vari-ables which distributions belong to the class F∈C!F∈L∩D!F∈S, respectively.Based on these results, we obtain the uniform asymptotic of the weighted sums of de-pendent random variables under the assumption that the distributions belong to theclass of subexponential distributions.