Tails of the Moments for Sums with Dominatedly Varying Random Summands

The asymptotic behaviour of the tail expectation ?E(Sn?)??{Sn?>x} is investigated, where exponent ? a nonnegative real number and Sn?=?1+…+?n sum dominatedly varying not necessarily identically distributed random summands, following specific dependence structure. It turns out that such can be asymptotically bounded from above below by sums expectations ?E?i??{?i>x} with correcting constants. obtained results are extended to case randomly weighted sums, collections weights primary variables independent. For illustration obtained, some particular examples given, between modelled in copulas framework.