A note on the asymptotics for the randomly stopped weighted sums
Yang Yang
Nanjing Audit University, China
Xi Xi Shi
Nanjing Audit University, China
Xing Fang Huang
Nanjing Audit University, China
Published 2018-04-12


randomly weighted sums
heavy tail
widely orthant dependence

How to Cite

Yang Y., Shi X. X. and Huang X. F. (2018) “A note on the asymptotics for the randomly stopped weighted sums”, Nonlinear Analysis: Modelling and Control, 23(2), pp. 204-212. doi: 10.15388/NA.2018.2.4.


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.

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