Expectation of the truncated randomly weighted sums with dominatedly varying summands

Tails of the Moments for Sums with Dominatedly Varying Random Summands

“…. , ξ n satisfy the so-called Assumption A (as in [4]), which was referred to later as a strong quasi-asymptotic independence in other articles (e.g., [6,7,16,44]), as well.…”

“…∑ n k=1 P(ξ k > x) and ∑ n k=1 P(θ k ξ k > x), respectively (see, e.g., [1][2][3][4][5][6][7][8][9][10][11]). The main results from the majority of the aforementioned papers are reviewed in detail in Section 3.…”

“…The main results from the majority of the aforementioned papers are reviewed in detail in Section 3. In line with the tail probabilities P S ξ n > x and P S θξ n > x , asymptotics of the tail expectations E S ξ n 1 {S ξ n >x} and E S θξ n 1 {S θξ n >x} are investigated in the literature; however, the number of papers is relatively scarce (see [6,7,12] and the references therein).…”

“…We recall these important indices. The first one is a so-called L-index, used in, e.g., [6,7,11,33,34]. The L F index for d.f.…”

“…The second important index is the upper Matuszewska index introduced in [35]. In this paper, we stick with the slightly different but equivalent formulation given in [36] and used in many other articles (e.g., [2,6,8,11,34]). For a d.f.…”