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Title: | Multivariate Normal Approximation on the Wiener Space: New Bounds in the Convex Distance |
Authors: | Nourdin, I Peccati, G Yang, X |
Keywords: | Breuer–Major theorem;convex distance;fourth moment theorems;Gaussian fields;Malliavin–Stein method;multidimensional normal approximations |
Issue Date: | 4-Jun-2021 |
Publisher: | Springer Nature |
Citation: | Nourdin, I., Peccati, G. and Yang, X. (2021) 'Multivariate Normal Approximation on the Wiener Space: New Bounds in the Convex Distance', Journal of Theoretical Probability, 0 (in press), pp. 1-18. doi.org/10.1007/s10959-021-01112-6 |
Abstract: | Copyright © The Author(s) 2021. We establish explicit bounds on the convex distance between the distribution of a vector of smooth functionals of a Gaussian field and that of a normal vector with a positive-definite covariance matrix. Our bounds are commensurate to the ones obtained by Nourdin et al. (Ann Inst Henri Poincaré Probab Stat 46(1):45–58, 2010) for the (smoother) 1-Wasserstein distance, and do not involve any additional logarithmic factor. One of the main tools exploited in our work is a recursive estimate on the convex distance recently obtained by Schulte and Yukich (Electron J Probab 24(130):1–42, 2019). We illustrate our abstract results in two different situations: (i) we prove a quantitative multivariate fourth moment theorem for vectors of multiple Wiener–Itô integrals, and (ii) we characterize the rate of convergence for the finite-dimensional distributions in the functional Breuer–Major theorem. |
URI: | https://bura.brunel.ac.uk/handle/2438/23858 |
DOI: | https://doi.org/10.1007/s10959-021-01112-6 |
ISSN: | 0894-9840 |
Appears in Collections: | Dept of Mathematics Research Papers |
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