Generalization of the Nualart-Peccati criterion

@article{Azmoodeh2016GeneralizationOT,
  title={Generalization of the Nualart-Peccati criterion},
  author={E. Azmoodeh and Dominique Malicet and G. Mijoule and Guillaume Poly},
  journal={Annals of Probability},
  year={2016},
  volume={44},
  pages={924-954}
}
The celebrated Nualart–Peccati criterion [Ann. Probab. 33 (2005) 177–193] ensures the convergence in distribution toward a standard Gaussian random variable N of a given sequence {Xn}n≥1 of multiple Wiener–Ito integrals of fixed order, if E[X2n]→1 and E[X4n]→E[N4]=3. Since its appearance in 2005, the natural question of ascertaining which other moments can replace the fourth moment in the above criterion has remained entirely open. Based on the technique recently introduced in [J. Funct. Anal… Expand
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