Precise Large Deviations For Sums Of WUOD And Φ-mixing Random Variables With Dominated Variation

The study of precise large deviations theory has a important significance in insurance.Up until now,many researchers made great efforts in the area of precise large deviations and had a lot of inspiring results.According to the two-eight principle in finance,many financial events are subject to the heavy-tailed distribution,so the assumption of heavy-tailed distribution is more realistic than the assumption of normal or lognormal distribution.Many scholars have focused on heavy-tail distribution and precise large deviations.Independent event is popular to be used as dependent structure assumption in the research field at present.But in practice,conditions of independent event are too strict.So that,there are few events that satisfy independent conditions.Therefore,the study of other dependent structures is particularly crucial.Up till the present moment,Φ-mixing sequence are intensively applied into statistical inference.However,little results about Φ-mixing sequence are used in applications of precise large deviations.Moreover,the asymptotic results about dominated variation,Φ-mixing sequence are very little,respectively.In this paper,we investigate the precise large deviations for sums of not identical distributed random variables which are widely upper orthant dependent(WUOD,in short)and Φ-mixing.The asymptotic relations for sums of random variables with dominated variation and consistently varying tail are obtained.What’s more,we verify the main results by simulations.