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1 Department of Mathematics Lawrence, Kansas 2 BIGS - Biology, genetics and statistics Inria Nancy - Grand Est, IECL - Institut Élie Cartan de Lorraine 3 Probabilités et statistiques IECL - Institut Élie Cartan de Lorraine 4 School of Finance and Statistics

Abstract : Consider a Gaussian stationary sequence with unit variance X. Assume that the central limit theorem holds for a weighted sum of elements of the form fX k, where f designates a finite sum of Hermite polynomials. Then we prove that the uniform convergence of the density of this weighted sum towards the standard Gaussian density also holds true, under a mild additional assumption involving the causal representation of X.





Autor: Yaozhong Hu - David Nualart - Samy Tindel - Fangjun Xu -

Fuente: https://hal.archives-ouvertes.fr/



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