I think, the old Markushevich's book on Analytic Functions is a good source of techniques and results in general. However, many particular cases may not fit those frames and may require specific analysis.
Best regards, Boyan.
All Tauberian Theorems give asymptotic behavior of the tail on infinity basing on corresponding behavior of characteristic function at zero. Both type of behavior cannot be verified by statistical methods. This is main point for this project. The problem is how to change the notion of the tail to obtain something siutable for statistical verification.
Thank you!
Lev
Another point (exaggerated): asymptotic methods have nothing common with statistics. The reason is that we almost never have uniform convergence to limit distribution among a large class of distributions.
Well, but you wrote that you have Probability generating functions. In my opinion, this is sufficient to get assymptotics in n --> infinity, or in large x.
No, this is a mistake. I do not have probability generating function when discussing heavy tails. May be it is mentioned in the text of my talk, but this talk is partially connected to the problem under discussion. Of course, I may use statistical estimator for probability generating function (and/or for characteristic function), but it is not enough to obtain asymptotic behavior of the tail.
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