Moderate Deviations For The Random Weighted Sums Of WUOD Random Variables With Consistently Varying Tails

The research of large deviations and moderate deviations for random sums and random weighted sums of random variables plays an important role in the field of financial risk,as well as probability and statistics.Many scholars have made breakthrough research results in this respect.The research on the subexponentiality of the product of independent random variables is of milestone significance,which lays a foundation for the research of other scholars.The study on the large deviations of heavy-tailed random variables relates the large deviations to heavy-tailed random variables,which provides a new idea for the future research work.Based on previous research results,a breakthrough has been made in the application of the random variables with heavy-tailed distributions in the field of financial risk,such as the study of the discretetime model with heavy-tailed insurance and financial risks.In this paper,the concepts of the heavy-tailed distributions mainly include the dominated variation class and the consistent variation class.In addition,the research on the dependence of random variables is also very important in probability and statistics.At present,there are a lot of research results on independent random variables,negative dependent random variables,END random variables and wide dependent random variables.Therefore,we can find that the research on random variables has been very in-depth and tends to be multidirectional.On this basis,we study the WUOD random variables with consistently varying tails.For se-quences of real-valued random variables {Xk,k?1} and sequences of positive random variables {?k,k?1},we write the random weighted sums of random variables as SN,?(t)=?k=1 N(t)?kXk,t?0,where {N(t),t?0} denotes a counting process.When N{t)=n for all t?0,we write Sn,?{t)=?k=1 n ?kXk.Two main conclusions are drawn:1,the asymptotic relations of moderate deviations for nonrandom weighted sums S n,?(t);2,the asymptotic relations of moderate devia-tions for random weighted sums S N,?(t).In addition,numerical simulation is given to verify the correctness of the conclusion.