Convergence rate in the splitting-up method for rough differential equations
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915042305245184 |
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| author | Pang, Peter H. C. |
| author_facet | Pang, Peter H. C. |
| contents | In this note we construct solutions to rough differential equations ${\rm d} Y = f(Y) \,{\rm d} X$ with a driver $X \in C^α([0,T];\mathbb{R}^d)$, $\frac13 < α\le \frac12$, using a splitting-up scheme. We show convergence of our scheme to solutions in the sense of Davie by a new argument and give a rate of convergence. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_00432 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convergence rate in the splitting-up method for rough differential equations Pang, Peter H. C. Classical Analysis and ODEs Numerical Analysis Probability 60L20, 60H35, 65C30 In this note we construct solutions to rough differential equations ${\rm d} Y = f(Y) \,{\rm d} X$ with a driver $X \in C^α([0,T];\mathbb{R}^d)$, $\frac13 < α\le \frac12$, using a splitting-up scheme. We show convergence of our scheme to solutions in the sense of Davie by a new argument and give a rate of convergence. |
| title | Convergence rate in the splitting-up method for rough differential equations |
| topic | Classical Analysis and ODEs Numerical Analysis Probability 60L20, 60H35, 65C30 |
| url | https://arxiv.org/abs/2412.00432 |