A strong Tauberian theorem for characteristic functions

R Riedi 1 Paulo Gonçalves 2
2 DANTE - Dynamic Networks : Temporal and Structural Capture Approach
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme, IXXI - Institut Rhône-Alpin des systèmes complexes
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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R Riedi, Paulo Gonçalves. A strong Tauberian theorem for characteristic functions. Applied and Computational Harmonic Analysis, Elsevier, 2015, 39, pp.6. ⟨10.1016/j.acha.2015.03.007⟩. ⟨hal-01245436⟩

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