Convergence of the tamed-Euler-Maruyama method for SDEs with discontinuous and polynomially growing drift
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| Format: | Preprint |
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2022
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| _version_ | 1866909067995250688 |
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| author | Spendier, Kathrin Szölgyenyi, Michaela |
| author_facet | Spendier, Kathrin Szölgyenyi, Michaela |
| contents | Numerical methods for SDEs with irregular coefficients are intensively studied in the literature, with different types of irregularities usually being attacked separately. In this paper we combine two different types of irregularities: polynomially growing drift coefficients and discontinuous drift coefficients. For SDEs that suffer from both irregularities we prove strong convergence of order $1/2$ of the tamed-Euler-Maruyama scheme from [Hutzenthaler, M., Jentzen, A., and Kloeden, P. E., The Annals of Applied Probability, 22(4):1611-1641, 2012]. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2212_08839 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Convergence of the tamed-Euler-Maruyama method for SDEs with discontinuous and polynomially growing drift Spendier, Kathrin Szölgyenyi, Michaela Numerical Analysis Probability 60H10, 65C30 Numerical methods for SDEs with irregular coefficients are intensively studied in the literature, with different types of irregularities usually being attacked separately. In this paper we combine two different types of irregularities: polynomially growing drift coefficients and discontinuous drift coefficients. For SDEs that suffer from both irregularities we prove strong convergence of order $1/2$ of the tamed-Euler-Maruyama scheme from [Hutzenthaler, M., Jentzen, A., and Kloeden, P. E., The Annals of Applied Probability, 22(4):1611-1641, 2012]. |
| title | Convergence of the tamed-Euler-Maruyama method for SDEs with discontinuous and polynomially growing drift |
| topic | Numerical Analysis Probability 60H10, 65C30 |
| url | https://arxiv.org/abs/2212.08839 |