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| Autori principali: | , , |
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| Natura: | Preprint |
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2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2504.19192 |
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| _version_ | 1866918001538760704 |
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| author | Chen, Ziheng Liu, Jiao Wu, Anxin |
| author_facet | Chen, Ziheng Liu, Jiao Wu, Anxin |
| contents | This work investigates the strong and weak convergence orders of numerical methods for SDEs driven by time-changed Lévy noise under the globally Lipschitz conditions. Based on the duality theorem, we prove that the numerical approximation generated by the stochastic $θ$ method with $θ\in [0,1]$ and the simulation of inverse subordinator converges strongly with order $1/2$. Moreover, the numerical approximation combined with the Euler--Maruyama method and the estimate of inverse subordinator is shown to have the weak convergence order $1$ by means of the Kolmogorov backward partial integro differential equations. These theoretical results are finally confirmed by some numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19192 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Strong and weak convergence orders of numerical methods for SDEs driven by time-changed Lévy noise Chen, Ziheng Liu, Jiao Wu, Anxin Numerical Analysis This work investigates the strong and weak convergence orders of numerical methods for SDEs driven by time-changed Lévy noise under the globally Lipschitz conditions. Based on the duality theorem, we prove that the numerical approximation generated by the stochastic $θ$ method with $θ\in [0,1]$ and the simulation of inverse subordinator converges strongly with order $1/2$. Moreover, the numerical approximation combined with the Euler--Maruyama method and the estimate of inverse subordinator is shown to have the weak convergence order $1$ by means of the Kolmogorov backward partial integro differential equations. These theoretical results are finally confirmed by some numerical experiments. |
| title | Strong and weak convergence orders of numerical methods for SDEs driven by time-changed Lévy noise |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2504.19192 |