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July 2009 Noncentral convergence of multiple integrals
Ivan Nourdin, Giovanni Peccati
Ann. Probab. 37(4): 1412-1426 (July 2009). DOI: 10.1214/08-AOP435

Abstract

Fix ν>0, denote by G(ν/2) a Gamma random variable with parameter ν/2 and let n≥2 be a fixed even integer. Consider a sequence {Fk}k≥1 of square integrable random variables belonging to the nth Wiener chaos of a given Gaussian process and with variance converging to 2ν. As k→∞, we prove that Fk converges in distribution to 2G(ν/2)−ν if and only if E(Fk4)−12E(Fk3)→12ν2−48ν.

Citation

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Ivan Nourdin. Giovanni Peccati. "Noncentral convergence of multiple integrals." Ann. Probab. 37 (4) 1412 - 1426, July 2009. https://doi.org/10.1214/08-AOP435

Information

Published: July 2009
First available in Project Euclid: 21 July 2009

zbMATH: 1171.60323
MathSciNet: MR2546749
Digital Object Identifier: 10.1214/08-AOP435

Subjects:
Primary: 60F05, 60G15, 60H05, 60H07

Rights: Copyright © 2009 Institute of Mathematical Statistics

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Vol.37 • No. 4 • July 2009
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