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

Benjamin Arras, Ehsan Azmoodeh, Guillaume Poly and Yvik Swan

Stochastic Processes and their Applications, 2019, vol. 129, issue 7, 2341-2375

Abstract: We provide a bound on a distance between finitely supported elements and general elements of the unit sphere of ℓ2(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 the second Wiener chaos. In particular, we explicit these rates for non-central asymptotic of sequences of quadratic forms and the behavior of the generalized Rosenblatt process at extreme critical exponent.

Keywords: Second Wiener chaos; Variance-gamma distribution; Wasserstein-2 distance; Malliavin Calculus; Stein discrepancy (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:129:y:2019:i:7:p:2341-2375

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DOI: 10.1016/j.spa.2018.07.009

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