Geometric Ergodicity and Strong Error Estimates for Tamed Schemes of Super-linear SODEs
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910692390469632 |
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| author | Liu, Zhihui Wu, Xiaoming |
| author_facet | Liu, Zhihui Wu, Xiaoming |
| contents | We construct a family of explicit tamed Euler--Maruyama (TEM) schemes, which can preserve the same Lyapunov structure for super-linear stochastic ordinary differential equations (SODEs) driven by multiplicative noise.These TEM schemes are shown to inherit the geometric ergodicity of the considered SODEs and converge with optimal strong convergence orders. Numerical experiments verify our theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_06049 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Geometric Ergodicity and Strong Error Estimates for Tamed Schemes of Super-linear SODEs Liu, Zhihui Wu, Xiaoming Numerical Analysis 65C30, 60H35, 60H10 We construct a family of explicit tamed Euler--Maruyama (TEM) schemes, which can preserve the same Lyapunov structure for super-linear stochastic ordinary differential equations (SODEs) driven by multiplicative noise.These TEM schemes are shown to inherit the geometric ergodicity of the considered SODEs and converge with optimal strong convergence orders. Numerical experiments verify our theoretical results. |
| title | Geometric Ergodicity and Strong Error Estimates for Tamed Schemes of Super-linear SODEs |
| topic | Numerical Analysis 65C30, 60H35, 60H10 |
| url | https://arxiv.org/abs/2411.06049 |