Tails of higher-order moments with dominatedly varying summands

摘要

Let xi(1), . . . , xi(n) be dependent real -valued random variables with dominatedly varying distribution functions. We investigate the asymptotic behavior of the tail-moment E((S-n(xi))(m)1({Sn xi >x})), where m is a nonnegative integer, and S-n(xi) = xi(1) + . . . + xi(n). We consider the dependence structure, similar to pairwise strongly quasiasymptotic independence among the random summands. We also study the case where each summand of S-n(xi) can be expressed as the product of two random variables.