On the Gaussian approximation of vector-valued multiple integrals

  title={On the Gaussian approximation of vector-valued multiple integrals},
  author={Salim Noreddine and Ivan Nourdin},
  journal={J. Multivariate Analysis},
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

From This Paper

Topics from this paper.


Publications referenced by this paper.
Showing 1-10 of 10 references

Stein's method on

  • I. Nourdin, G. Peccati
  • Wiener chaos. Probab. Theory Relat. Fields 145,
  • 2009
1 Excerpt

Central limit theorems for multiple stochastic integrals and Malliavin calculus

  • S. D. Nualart
  • Ortiz-Latorre
  • 2008
2 Excerpts

The Malliavin calculus and related topics. Springer-Verlag, Berlin, 2nd edition

  • D. Nualart
  • 2006
2 Excerpts

Multiple stochastic integrals with dependent integrators

  • M.S.R. Fox
  • Taqqu
  • 1987

Similar Papers

Loading similar papers…