On the convergence order of the Euler scheme for scalar SDEs with Hölder-type diffusion coefficients
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866916090835107840 |
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| author | Mickel, Annalena Neuenkirch, Andreas |
| author_facet | Mickel, Annalena Neuenkirch, Andreas |
| contents | We study the Euler scheme for scalar non-autonomous stochastic differential equations, whose diffusion coefficient is not globally Lipschitz but a fractional power of a globally Lipschitz function. We analyse the strong error and establish a criterion, which relates the convergence order of the Euler scheme to an inverse moment condition for the diffusion coefficient. Our result in particular applies to Cox-Ingersoll-Ross-, Chan-Karolyi-Longstaff-Sanders- or Wright-Fisher-type stochastic differential equations and thus provides a unifying framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_11448 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the convergence order of the Euler scheme for scalar SDEs with Hölder-type diffusion coefficients Mickel, Annalena Neuenkirch, Andreas Numerical Analysis Probability 65C30, 60H35 We study the Euler scheme for scalar non-autonomous stochastic differential equations, whose diffusion coefficient is not globally Lipschitz but a fractional power of a globally Lipschitz function. We analyse the strong error and establish a criterion, which relates the convergence order of the Euler scheme to an inverse moment condition for the diffusion coefficient. Our result in particular applies to Cox-Ingersoll-Ross-, Chan-Karolyi-Longstaff-Sanders- or Wright-Fisher-type stochastic differential equations and thus provides a unifying framework. |
| title | On the convergence order of the Euler scheme for scalar SDEs with Hölder-type diffusion coefficients |
| topic | Numerical Analysis Probability 65C30, 60H35 |
| url | https://arxiv.org/abs/2307.11448 |