A bound on the Wasserstein-2 distance between linear combinations of independent random variables

@article{Arras2019ABO,
  title={A bound on the Wasserstein-2 distance between linear combinations of independent random variables},
  author={B. Arras and E. Azmoodeh and Guillaume Poly and Yvik Swan},
  journal={Stochastic Processes and their Applications},
  year={2019},
  volume={129},
  pages={2341-2375}
}
Abstract We provide a bound on a distance between finitely supported elements and general elements of the unit sphere of l 2 ( N ∗ ) . We use this bound to estimate the Wasserstein-2 distance between random variables represented by linear combinations of independent random variables. Our results are expressed in terms of a discrepancy measure related to Nourdin–Peccati’s Malliavin–Stein method. The main application is towards the computation of quantitative rates of convergence to elements of… Expand
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