On The Expansion Of Large Deviation Of Random Walk With High Order General Regular Variation Tails

In this paper high order general regular variation condition is proposed.Under this condition, the large deviation probabilities for the sums and the maxima of partial sums of independent and identically distributed(i.i.d) random variables are investigated, and condition [D_k] is improved.In chapter 1, we introduce some presumptions and some known results.In chapter 2, we give the high order general regular variation conditionfrom the definition of high order general regular variation and its properties.In chapter 3, under the high order general regular variation condition,we obtain the estimation of V_n(x) (?) P{S_n > x} and V_n(x) (?) P{S_n > x} in different way.