A note on the asymptotics for the randomly stopped weighted sums - Yang, Yang; Shi, Xi Xi Xi; Huang, Xing Fang Fang (Nonlinear Analysis: Modelling and Control, 2018)
Let Xi , i ⩾ 1 be a sequence of identically distributed real-valued random variables with common distribution FX; let θi , i ⩾ 1 be a sequence of identically distributed, nonnegative and nondegenerate at zero random variables; and let τ be a positive integer-valued counting random variable. Assume that Xi , i ⩾ 1, θi , i ⩾ 1 and τ are mutually independent. In the presence of heavy-tailed Xi’s, this paper investigates the asymptotic tail behavior for the maximum of randomly weighted sums Mτ = max1 ⩽ k ⩽ τ ∑ki = 1θi Xi under the condition that θi , i ⩾ 1 satisfy a general dependence structure.