## Strong asymptotic independence on Wiener chaos

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- by Ivan Nourdin, David Nualart and Giovanni Peccati PDF
- Proc. Amer. Math. Soc.
**144**(2016), 875-886 Request permission

## Abstract:

Let $F_n = (F_{1,n}, \dots ,F_{d,n})$, $n\geqslant 1$, be a sequence of random vectors such that, for every $j=1,\dots ,d$, the random variable $F_{j,n}$ belongs to a fixed Wiener chaos of a Gaussian field. We show that, as $n\to \infty$, the components of $F_n$ are asymptotically independent if and only if $\mathrm {Cov}(F_{i,n}^2,F_{j,n}^2)\to 0$ for every $i\neq j$. Our findings are based on a novel inequality for vectors of multiple Wiener-Itô integrals, and represent a substantial refining of criteria for asymptotic independence in the sense of moments recently established by Nourdin and Rosiński (2014).## References

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## Additional Information

**Ivan Nourdin**- Affiliation: Université du Luxembourg, Unité de Recherche en Mathématiques, 6 rue Richard Coudenhove-Kalergi, L-1359, Luxembourg
- MR Author ID: 730973
- Email: ivan.nourdin@uni.lu
**David Nualart**- Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas 66045
- MR Author ID: 132560
- Email: nualart@math.ku.edu
**Giovanni Peccati**- Affiliation: Université du Luxembourg, Unité de Recherche en Mathématiques, 6 rue Richard Coudenhove-Kalergi, L-1359, Luxembourg
- MR Author ID: 683104
- Email: giovanni.peccati@gmail.com
- Received by editor(s): January 8, 2014
- Received by editor(s) in revised form: January 12, 2015
- Published electronically: October 6, 2015
- Additional Notes: The first author was partially supported by the ANR Grant ANR-10-BLAN-0121.

The second author was partially supported by the NSF grant DMS1208625.

The third author was partially supported by the grant F1R-MTH-PUL-12PAMP (PAMPAS), from Luxembourg University - Communicated by: Mark M. Meerschaert
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**144**(2016), 875-886 - MSC (2010): Primary 60F05, 60H07, 60G15
- DOI: https://doi.org/10.1090/proc12769
- MathSciNet review: 3430861