References & Citations
Mathematics > Probability
Title: A new approach in two-dimensional heavy-tailed distributions
(Submitted on 14 Feb 2024 (v1), last revised 26 Apr 2024 (this version, v2))
Abstract: We consider a new approach in the definition of two-dimensional heavy-tailed distributions. Namely, we introduce the classes of two-dimensional long-tailed, of twodimensional dominatedly varying and of two-dimensional consistently varying distributions. Next, we define the closure property with respect to two-dimensional convolution and to joint max-sum equivalence in order to study if they are satisfied by these classes. Further we examine the joint behavior of two random sums, under generalized tail asymptotic independence. Afterward we study the closure property under scalar product and two dimensional product convolution and by these results we extended our main result in the case of jointly randomly weighted sums. Our results contained some applications where we establish the asymptotic expression of the ruin probability in a two-dimensional discrete-time risk model.
Submission history
From: Charalampos D. Passalidis [view email][v1] Wed, 14 Feb 2024 09:35:29 GMT (23kb)
[v2] Fri, 26 Apr 2024 15:55:14 GMT (23kb)
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