Optimal Gamma Approximation on Wiener Space

  title={Optimal Gamma Approximation on Wiener Space},
  author={Ehsan Azmoodeh and Peter Eichelsbacher and Lukas Knichel},
  journal={arXiv: Probability},
In \cite{n-p-noncentral}, Nourdin and Peccati established a neat characterization of Gamma approximation on a fixed Wiener chaos in terms of convergence of only the third and fourth cumulants. In this paper, we provide an optimal rate of convergence in the $d_2$-distance in terms of the maximum of the third and fourth cumulants analogous to the result for normal approximation in \cite{n-p-optimal}. In order to achieve our goal, we introduce a novel operator theory approach to Stein's method… Expand
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