On the rate of convergence for an $α$-stable central limit theorem under sublinear expectation
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866909220546281472 |
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| author | Hu, Mingshang Jiang, Lianzi Liang, Gechun |
| author_facet | Hu, Mingshang Jiang, Lianzi Liang, Gechun |
| contents | In this paper, we propose a monotone approximation scheme for a class of fully nonlinear degenerate partial integro-differential equations (PIDEs) which characterize the nonlinear $α$-stable Lévy processes under sublinear expectation space with $α\in(1,2)$. 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 $α$-stable central limit theorem under sublinear expectation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_11076 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On the rate of convergence for an $α$-stable central limit theorem under sublinear expectation Hu, Mingshang Jiang, Lianzi Liang, Gechun Probability Numerical Analysis 60F05, 60E07, 65M15 In this paper, we propose a monotone approximation scheme for a class of fully nonlinear degenerate partial integro-differential equations (PIDEs) which characterize the nonlinear $α$-stable Lévy processes under sublinear expectation space with $α\in(1,2)$. 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 $α$-stable central limit theorem under sublinear expectation. |
| title | On the rate of convergence for an $α$-stable central limit theorem under sublinear expectation |
| topic | Probability Numerical Analysis 60F05, 60E07, 65M15 |
| url | https://arxiv.org/abs/2107.11076 |