Strong convergence of the Euler scheme for singular kinetic SDEs driven by $\alpha$-stable processes
| Autor: | Ling, Chengcheng |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | We study the strong approximation of the solutions to singular stochastic kinetic equations (also referred to as second-order SDEs) driven by $\alpha$-stable processes, using an Euler-type scheme inspired by [11]. For these equations, the stability index $\alpha$ lies in the range $(1,2)$, and the drift term exhibits anisotropic $\beta$-H\"older continuity with $\beta >1 - \frac{\alpha}{2}$. We establish a convergence rate of $(\frac{1}{2} + \frac{\beta}{\alpha(1+\alpha)} \wedge \frac{1}{2})$, which aligns with the results in [4] concerning first-order SDEs. Comment: 28 pages |
| Databáze: | arXiv |
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