Please use this identifier to cite or link to this item:
http://bura.brunel.ac.uk/handle/2438/24508
Title: | Non-integrable Stable Approximation by Stein’s Method |
Authors: | Chen, P Nourdin, I Xu, L Yang, X Zhang, R |
Keywords: | α-stable approximation;Stein’s method;Generalized central limit theorem;Rate of convergence;Fractional Laplacian;Normal attraction;Leave-one-out approach;Truncation |
Issue Date: | 3-Mar-2021 |
Publisher: | Springer |
Citation: | Chen, P., Nourdin, I., Xu, L. et al. Non-integrable Stable Approximation by Stein’s Method. J Theor Probab (2021). https://doi.org/10.1007/s10959-021-01094-5 |
Abstract: | We develop Stein’s method for α-stable approximation with α ∈ (0, 1], continuing the recent line of research by Xu [40] and Chen, Nourdin and Xu [11] in the case α ∈ (1, 2). The main results include an intrinsic upper bound for the error of the approximation in a variant of Wasserstein distance that involves the characterizing differential operators for stable distributions, and an application to the generalized central limit theorem. Due to the lack of first moment for the approximating sequence in the latter result, we appeal to an additional truncation procedure and investigate fine regularity properties of the solution to |
URI: | http://bura.brunel.ac.uk/handle/2438/24508 |
DOI: | http://dx.doi.org/10.1007/s10959-021-01094-5 https://doi.org/10.48550/arXiv.1903.12315 |
ISSN: | 0894-9840 1572-9230 |
Appears in Collections: | Dept of Mathematics Research Papers |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
FullText.pdf | 339.95 kB | Adobe PDF | View/Open |
Items in BURA are protected by copyright, with all rights reserved, unless otherwise indicated.