Uniform Approximation for the Tail Behavior of Bidimensional Randomly Weighted Sums

Xinmei Shen () and Kailin Du ()
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Xinmei Shen: Dalian University of Technology
Kailin Du: Dalian University of Technology

Methodology and Computing in Applied Probability, 2023, vol. 25, issue 1, 1-25

Abstract: Abstract The uniform approximation for the tail behavior of bidimensional randomly weighted sums is considered in this paper. The primary random vectors are supposed to have extended regularly varying tails, while the underlying dependence between the components is described by some quasi-extended-regular-variation (QERV) copula functions. There are mild moment conditions on the random weight vectors without any assumptions on the dependence structures between themselves. The case when the number of the sums is extended to an integer-valued random variable is investigated additionally. A direct application of the results in a stochastic difference equation and some numerical simulations are also stated.

Keywords: Uniform asymptotic; Extended regular variation; Bidimensional randomly weighted sum; Tail probability; Primary 62E20; Secondary 60E05 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11009-023-10000-x

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