Density convergence in the Breuer-Major theorem for Gaussian stationary sequences
Résumé
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 f(X_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.
Domaines
Probabilités [math.PR]| Origine | Fichiers produits par l'(les) auteur(s) |
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