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arXiv · 1701.06766

Weak convergence on Wiener space: targeting the first two chaoses

Christian Krein
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Abstract

We consider sequences of random variables living in a finite sum of Wiener chaoses. We find necessary and sufficient conditions for convergence in law to a target variable living in the sum of the first two Wiener chaoses. Our conditions hold notably for sequences of multiple Wiener integrals. Malliavin calculus and in particular the Gamma-operators are used. Our results extend previous findings by Azmoodeh, Peccati and Poly (2014) and are applied to central and non-central convergence situations. Our methods are applied as well to investigate stable convergence. We finally exclude certain classes of random variables as target variables for sequences living in a fixed Wiener chaos.

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Christian Krein. 2017-01-24. Weak convergence on Wiener space: targeting the first two chaoses. https://doi.org/10.30757/alea.v16-05

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