Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1155836 | Stochastic Processes and their Applications | 2012 | 25 Pages |
Abstract
Consider the sum Z=∑n=1∞λn(ηn−Eηn), where ηnηn are independent gamma random variables with shape parameters rn>0rn>0, and the λnλn’s are predetermined weights. We study the asymptotic behavior of the tail ∑n=M∞λn(ηn−Eηn), which is asymptotically normal under certain conditions. We derive a Berry–Esseen bound and Edgeworth expansions for its distribution function. We illustrate the effectiveness of these expansions on an infinite sum of weighted chi-squared distributions.The results we obtain are directly applicable to the study of double Wiener–Itô integrals and to the “Rosenblatt distribution”.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Mark S. Veillette, Murad S. Taqqu,