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1 Probabilités et statistiques IECL - Institut Élie Cartan de Lorraine 2 FSTC - Faculté des Sciences, de la Technologie et de la Communication

Abstract : We compute the exact rates of convergence in total variation associated with the -fourth moment theorem- by Nualart and Peccati 2005, stating that a sequence of random variables living in a fixed Wiener chaos verifies a central limit theorem CLT if and only if the sequence of the corresponding fourth cumulants converges to zero. We also provide an explicit illustration based on the Breuer-Major CLT for Gaussian-subordinated random sequences.

Keywords : Berry-Esseen bounds Central Limit Theorem Fourth Moment Theorem Gaussian Fields Stein-s method Total variation





Author: Ivan Nourdin - Giovanni Peccati -

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



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