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September 2010 Invariance principles for homogeneous sums: Universality of Gaussian Wiener chaos
Ivan Nourdin, Giovanni Peccati, Gesine Reinert
Ann. Probab. 38(5): 1947-1985 (September 2010). DOI: 10.1214/10-AOP531

Abstract

We compute explicit bounds in the normal and chi-square approximations of multilinear homogenous sums (of arbitrary order) of general centered independent random variables with unit variance. In particular, we show that chaotic random variables enjoy the following form of universality: (a) the normal and chi-square approximations of any homogenous sum can be completely characterized and assessed by first switching to its Wiener chaos counterpart, and (b) the simple upper bounds and convergence criteria available on the Wiener chaos extend almost verbatim to the class of homogeneous sums.

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Ivan Nourdin. Giovanni Peccati. Gesine Reinert. "Invariance principles for homogeneous sums: Universality of Gaussian Wiener chaos." Ann. Probab. 38 (5) 1947 - 1985, September 2010. https://doi.org/10.1214/10-AOP531

Information

Published: September 2010
First available in Project Euclid: 17 August 2010

zbMATH: 1246.60039
MathSciNet: MR2722791
Digital Object Identifier: 10.1214/10-AOP531

Subjects:
Primary: 60F05, 60F17, 60G15, 60H07

Rights: Copyright © 2010 Institute of Mathematical Statistics

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Vol.38 • No. 5 • September 2010
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