Weak convergence on Wiener space: targeting the first two chaoses

  title={Weak convergence on Wiener space: targeting the first two chaoses},
  author={Christian Yves L{\'e}opold Krein},
  journal={Latin American Journal of Probability and Mathematical Statistics},
  • C. Krein
  • Published 2019
  • Mathematics
  • Latin American Journal of Probability and Mathematical Statistics
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… Expand
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