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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 |
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