Stein’s method on Wiener chaos

@article{Nourdin2007SteinsMO,
  title={Stein’s method on Wiener chaos},
  author={Ivan Nourdin and Giovanni Peccati},
  journal={Probability Theory and Related Fields},
  year={2007},
  volume={145},
  pages={75-118}
}
We combine Malliavin calculus with Stein’s method, in order to derive explicit bounds in the Gaussian and Gamma approximations of random variables in a fixed Wiener chaos of a general Gaussian process. Our approach generalizes, refines and unifies the central and non-central limit theorems for multiple Wiener–Itô integrals recently proved (in several papers, from 2005 to 2007) by Nourdin, Nualart, Ortiz-Latorre, Peccati and Tudor. We apply our techniques to prove Berry–Esséen bounds in the… Expand
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