On the Gaussian approximation of vector-valued multiple integrals

@article{Noreddine2011OnTG,
  title={On the Gaussian approximation of vector-valued multiple integrals},
  author={Salim Noreddine and Ivan Nourdin},
  journal={J. Multivariate Analysis},
  year={2011},
  volume={102},
  pages={1008-1017}
}
By combining the ndings of two recent, seminal papers by Nualart, Peccati and Tudor, we get that the convergence in law of any sequence of vector-valued multiple integrals Fn towards a centered Gaussian random vector N , with given covariance matrix C, is reduced to just the convergence of: (i) the fourth cumulant of each component of Fn to zero; (ii) the covariance matrix of Fn to C. The aim of this paper is to understand more deeply this somewhat surprising phenomenom. To reach this goal, we… CONTINUE READING

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