Strong convergence of the Euler scheme for singular kinetic SDEs driven by $α$-stable processes
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866908655073361920 |
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| author | Ling, Chengcheng |
| author_facet | Ling, Chengcheng |
| contents | We study the strong approximation of the solutions to singular stochastic kinetic equations (also referred to as second-order SDEs) driven by $α$-stable processes, using an Euler-type scheme inspired by [11]. For these equations, the stability index $α$ lies in the range $(1,2)$, and the drift term exhibits anisotropic $β$-Hölder continuity with $β>1 - \fracα{2}$. We establish a convergence rate of $(\frac{1}{2} + \fracβ{α(1+α)} \wedge \frac{1}{2})$, which aligns with the results in [4] concerning first-order SDEs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_05142 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Strong convergence of the Euler scheme for singular kinetic SDEs driven by $α$-stable processes Ling, Chengcheng Probability Numerical Analysis Primary 60H35, 65C30, 60H10, Secondary 60H50, 60L90 We study the strong approximation of the solutions to singular stochastic kinetic equations (also referred to as second-order SDEs) driven by $α$-stable processes, using an Euler-type scheme inspired by [11]. For these equations, the stability index $α$ lies in the range $(1,2)$, and the drift term exhibits anisotropic $β$-Hölder continuity with $β>1 - \fracα{2}$. We establish a convergence rate of $(\frac{1}{2} + \fracβ{α(1+α)} \wedge \frac{1}{2})$, which aligns with the results in [4] concerning first-order SDEs. |
| title | Strong convergence of the Euler scheme for singular kinetic SDEs driven by $α$-stable processes |
| topic | Probability Numerical Analysis Primary 60H35, 65C30, 60H10, Secondary 60H50, 60L90 |
| url | https://arxiv.org/abs/2412.05142 |