Brunel University Research Archive(BURA) preserves and enables easy and open access to all
types of digital content. It showcases Brunel's research outputs.
Research contained within BURA is open access, although some publications may be subject
to publisher imposed embargoes. All awarded PhD theses are also archived on BURA.
Please use this identifier to cite or link to this item:
http://bura.brunel.ac.uk/handle/2438/29289| Title: | Multivariate Stable Approximation by Stein’s Method |
| Other Titles: | Multivariate stable approximation in Wasserstein distance by Stein's method |
| Authors: | Chen, P Nourdin, I Xu, L Yang, X |
| Keywords: | multivariate α-stable approximation;Stein’s method;generalized central limit theorem;rate of convergence;Wasserstein(-type) distance;fractional Laplacian |
| Issue Date: | 4-May-2023 |
| Publisher: | Springer Nature |
| Citation: | Chen, P. et al. (2024) 'Multivariate Stable Approximation by Stein’s Method', Journal of Theoretical Probability, 37 (1), pp. 446 - 488. doi: 10.1007/s10959-023-01244-x. |
| Abstract: | By a delicate analysis for the Stein's equation associated to the α-stable law approximation with α ∈ (0,2), we prove a quantitative stable central limit theorem in Wasserstein type distance, which generalizes the results in the series of work (Chen et al. in J Theor Probab 34(3):1382–1407, 2021; Chen et al. in J Theor Probab 35(2):1137–1186 2022; Xu in Ann Appl Probab 29(1):458–504, 2019) from the univariate case to the multiple variate case. From an explicit computation for Pareto’s distribution, we see that the rate of our approximation is sharp. The analysis of the Stein’s equation is new and has independent interest. |
| Description: | Data Availability: Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study. Mathematics Subject Classification :60E07; 60E17; 60F05; 60G52. The article version archived on this institutional repository is the accepted manuscript available online at: arXiv:1911.12917v2 [math.PR] (https://arxiv.org/abs/1911.12917v2) under the working title, 'Multivariate stable approximation in Wasserstein distance by Stein's method'. It has been certified by peer review. |
| URI: | https://bura.brunel.ac.uk/handle/2438/29289 |
| DOI: | https://doi.org/10.1007/s10959-023-01244-x |
| ISSN: | 0894-9840 |
| Other Identifiers: | ORCiD: Xiaochuan Yang https://orcid.org/0000-0003-2435-4615 arXiv:1911.12917v2 [math.PR] |
| Appears in Collections: | Dept of Mathematics Research Papers |
Files in This Item:
| File | Description | Size | Format | |
|---|---|---|---|---|
| FullText.pdf | Copyright© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2023. This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/s10959-023-01244-x (see: https://www.springernature.com/gp/open-research/policies/journal-policies). | 423.89 kB | Adobe PDF | View/Open |
Items in BURA are protected by copyright, with all rights reserved, unless otherwise indicated.