A strong Tauberian theorem for characteristic functions

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• 作者：R. Riedi^a ; ^{rudolf.riedi@hefr.ch" class="auth_mail" title="E-mail the corresponding author} ; P. Gonç ; alves^b ; ^{paulo.goncalves@inria.fr" class="auth_mail" title="E-mail the corresponding author}
• 刊名：Applied and Computational Harmonic Analysis
• 出版年：2015
• 出版时间：November 2015
• 年：2015
• 卷：39
• 期：3
• 页码：552-557
• 全文大小：262 K

文摘

Using wavelet analysis we show that if the characteristic function of a random variable X can be approximated at 0 by some polynomial of even degree 2p then the moment of order 2p of X exists. This strengthens a Tauberian-type result by Ramachandran and implies that the characteristic function is actually 2p times differentiable at 0. This fact also provides the theoretical basis for a wavelet based non-parametric estimator of the tail index of a distribution.