The Local Precise Large Deviation And Moderate Deviation For Random Sums

It is well known that large deviation theory and moderate deviation theory areones of the hot research issues in probabilistic theory. Most of the time, scholars con-centrated on studying global deviation theory, many results in this field have beenobtained. But for local deviation, some conclusions have been obtained based on spe-cial type of random variables. For example, Doney(1989), Baltrunas(1996), Lin(2008)considered local precise large deviation of integer-valued random variables, Yang etal.(2010), Li(2011) studied local precise large deviation for partial sums of continuousrandom variables. Recently,Li(2012) obtained local precise large deviation and mod-erate deviation for partial sums of general random variables. In this paper, we furtherdiscuss local precise large deviation and moderate deviation for random sums of generalrandom variables.In this paper, we obtain some results on local precise large deviation and moderatedeviation for random sums. First, according to the research ideas of global preciselarge deviation, we discuss local precise large deviation for random sums on the basis ofLi(2012), and our conclusion includes the global case. Second, similar to the discussionsof global deviation in Gao(2007), Liu(2010), we obtain local precise moderate deviationfor partial sums and also extend the result to the situation of random sums. Finally,we consider the asymptotic behavior of two risk models by using the obtained resultof local precise large deviation.