Weak error on the densities for the Euler scheme of stable additive SDEs with H{ö}lder drift
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913027568173056 |
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| author | Fitoussi, Mathis Menozzi, Stephane |
| author_facet | Fitoussi, Mathis Menozzi, Stephane |
| contents | We are interested in the Euler-Maruyama dicretization of the SDE dXt =b(t,Xt)dt+ dZt, X0 =x$\in$Rd, where Zt is a symmetric isotropic d-dimensional $α$-stable process, $α$ $\in$ (1, 2] and the drift b $\in$ L$\infty$ ([0,T],C$β$(Rd,Rd)), $β$ $\in$ (0,1), is bounded and H{ö}lder regular in space. Using an Euler scheme with a randomization of the time variable, we show that, denoting $γ$\,:= $α$ + $β$ -- 1, the weak error on densities related to this discretization converges at the rate $γ$/$α$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_10250 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weak error on the densities for the Euler scheme of stable additive SDEs with H{ö}lder drift Fitoussi, Mathis Menozzi, Stephane Numerical Analysis Probability We are interested in the Euler-Maruyama dicretization of the SDE dXt =b(t,Xt)dt+ dZt, X0 =x$\in$Rd, where Zt is a symmetric isotropic d-dimensional $α$-stable process, $α$ $\in$ (1, 2] and the drift b $\in$ L$\infty$ ([0,T],C$β$(Rd,Rd)), $β$ $\in$ (0,1), is bounded and H{ö}lder regular in space. Using an Euler scheme with a randomization of the time variable, we show that, denoting $γ$\,:= $α$ + $β$ -- 1, the weak error on densities related to this discretization converges at the rate $γ$/$α$. |
| title | Weak error on the densities for the Euler scheme of stable additive SDEs with H{ö}lder drift |
| topic | Numerical Analysis Probability |
| url | https://arxiv.org/abs/2410.10250 |