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Journal Articles Applied and Computational Harmonic Analysis Year : 2015

A strong Tauberian theorem for characteristic functions

Abstract

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.
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Dates and versions

hal-01245436 , version 1 (17-12-2015)

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R Riedi, Paulo Gonçalves. A strong Tauberian theorem for characteristic functions. Applied and Computational Harmonic Analysis, 2015, 39, pp.6. ⟨10.1016/j.acha.2015.03.007⟩. ⟨hal-01245436⟩
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