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On the rate of convergence for an α-stable central limit theorem under sublinear expectation

Part of: Distribution theory - Probability Limit theorems Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  03 October 2024

Mingshang Hu ,
Lianzi Jiang  and
Gechun Liang Open the ORCID record for Gechun Liang [Opens in a new window]
Mingshang Hu*
Affiliation:
Shandong University
Lianzi Jiang*
Affiliation:
Shandong University of Science and Technology
Gechun Liang*
Affiliation:
The University of Warwick
*
*Postal address: Zhongtai Securities Institute for Financial Studies, Shandong University, Jinan, Shandong 250100, PR China. Email: humingshang@sdu.edu.cn
**Postal address: College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, Shandong 266590, PR China. Email: jianglianzi95@163.com
***Postal address: Department of Statistics, The University of Warwick, Coventry CV4 7AL, UK. Email: g.liang@warwick.ac.uk
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Abstract

We propose a monotone approximation scheme for a class of fully nonlinear degenerate partial integro-differential equations which characterize nonlinear $\alpha$-stable Lévy processes under a sublinear expectation space with $\alpha\in(1,2)$. We further establish the error bounds for the monotone approximation scheme. This in turn yields an explicit Berry–Esseen bound and convergence rate for the $\alpha$-stable central limit theorem under sublinear expectation.

Keywords

Stable central limit theoremconvergence ratesublinear expectationmonotone scheme methodpartial integro-differential equation

MSC classification

Primary: 60F05: Central limit and other weak theorems
Secondary: 60E07: Infinitely divisible distributions; stable distributions 65M15: Error bounds
Type
Original Article
Information
Journal of Applied Probability , Volume 62 , Issue 1 , March 2025 , pp. 209 - 233
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Applied Probability Trust

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