A monotone scheme for G-equations with application to the explicit convergence rate of robust central limit theorem
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2019
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| _version_ | 1866917622892724224 |
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| author | Huang, Shuo Liang, Gechun |
| author_facet | Huang, Shuo Liang, Gechun |
| contents | We propose a monotone approximation scheme for a class of fully nonlinear PDEs called G-equations. Such equations arise often in the characterization of G-distributed random variables in a sublinear expectation space. The proposed scheme is constructed recursively based on a piecewise constant approximation of the viscosity solution to the G-equation. We establish the convergence of the scheme and determine the convergence rate with an explicit error bound, using the comparison principles for both the scheme and the equation together with a mollification procedure. The first application is obtaining the convergence rate of Peng's robust central limit theorem with an explicit bound of Berry-Esseen type. The second application is an approximation scheme with its convergence rate for the Black-Scholes-Barenblatt equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1904_07184 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | A monotone scheme for G-equations with application to the explicit convergence rate of robust central limit theorem Huang, Shuo Liang, Gechun Probability Numerical Analysis 60F05, 60H30, 65M15 We propose a monotone approximation scheme for a class of fully nonlinear PDEs called G-equations. Such equations arise often in the characterization of G-distributed random variables in a sublinear expectation space. The proposed scheme is constructed recursively based on a piecewise constant approximation of the viscosity solution to the G-equation. We establish the convergence of the scheme and determine the convergence rate with an explicit error bound, using the comparison principles for both the scheme and the equation together with a mollification procedure. The first application is obtaining the convergence rate of Peng's robust central limit theorem with an explicit bound of Berry-Esseen type. The second application is an approximation scheme with its convergence rate for the Black-Scholes-Barenblatt equation. |
| title | A monotone scheme for G-equations with application to the explicit convergence rate of robust central limit theorem |
| topic | Probability Numerical Analysis 60F05, 60H30, 65M15 |
| url | https://arxiv.org/abs/1904.07184 |