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DC Field | Value | Language |
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dc.contributor.author | Nourdin, I | - |
dc.contributor.author | Peccati, G | - |
dc.contributor.author | Yang, X | - |
dc.date.accessioned | 2021-12-31T16:36:05Z | - |
dc.date.available | 2021-12-31T16:36:05Z | - |
dc.date.issued | 2021-06-04 | - |
dc.identifier.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 | en_US |
dc.identifier.issn | 0894-9840 | - |
dc.identifier.uri | https://bura.brunel.ac.uk/handle/2438/23858 | - |
dc.description.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. | en_US |
dc.description.sponsorship | FNR grant APOGee (R-AGR-3585-10) at Luxembourg University; FNR grant FoRGES (R-AGR-3376-10) at Luxembourg University; FNR Grant MISSILe (R-AGR-3410-12-Z) at Luxembourg and Singapore Universities. | en_US |
dc.format.extent | 1 - 18 (18) | - |
dc.format.medium | Print-Electronic | - |
dc.language.iso | en_US | en_US |
dc.publisher | Springer Nature | en_US |
dc.rights | Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/. | - |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | - |
dc.subject | Breuer–Major theorem | en_US |
dc.subject | convex distance | en_US |
dc.subject | fourth moment theorems | en_US |
dc.subject | Gaussian fields | en_US |
dc.subject | Malliavin–Stein method | en_US |
dc.subject | multidimensional normal approximations | en_US |
dc.title | Multivariate Normal Approximation on the Wiener Space: New Bounds in the Convex Distance | en_US |
dc.type | Article | en_US |
dc.identifier.doi | https://doi.org/10.1007/s10959-021-01112-6 | - |
dc.relation.isPartOf | Journal of Theoretical Probability | - |
pubs.publication-status | Published | - |
pubs.volume | 0 | - |
dc.identifier.eissn | 1572-9230 | - |
Appears in Collections: | Dept of Mathematics Research Papers |
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