Arras, Benjamin, Azmoodeh, Ehsan 
ORCID: 0000-0002-0401-793X, Poly, Guillaume and Swan, Yvik
(2019)
A bound on the Wasserstein-2 distance between linear combinations of independent random variables.
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 129 (7).
pp. 2341-2375.
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Abstract
We provide a bound on a distance between finitely supported elements and general elements of the unit sphere of . 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.
| Item Type: | Article |
|---|---|
| Additional Information: | New section containing lower bounds |
| Uncontrolled Keywords: | Second Wiener chaos, Variance-gamma distribution, Wasserstein-2 distance, Malliavin Calculus, Stein discrepancy |
| Depositing User: | Symplectic Admin |
| Date Deposited: | 29 Apr 2020 09:16 |
| Last Modified: | 18 Jan 2023 23:54 |
| DOI: | 10.1016/j.spa.2018.07.009 |
| Related URLs: | |
| URI: | https://livrepository.liverpool.ac.uk/id/eprint/3084170 |
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