Convergence rate of numerical scheme for SDEs with a distributional drift in Besov space
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| Format: | Preprint |
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2023
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| _version_ | 1866917315437658112 |
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| author | Jáquez, Luis Mario Chaparro Issoglio, Elena Palczewski, Jan |
| author_facet | Jáquez, Luis Mario Chaparro Issoglio, Elena Palczewski, Jan |
| contents | This paper is concerned with numerical solutions of one-dimensional SDEs with the drift being a generalised function, in particular belonging to the Hölder-Zygmund space $C^{-γ}$ of negative order $-γ<0$ in the spatial variable. We design an Euler-Maruyama numerical scheme and prove its convergence, obtaining an upper bound for the strong $L^1$ convergence rate. We finally implement the scheme and discuss the results obtained. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2309_11396 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Convergence rate of numerical scheme for SDEs with a distributional drift in Besov space Jáquez, Luis Mario Chaparro Issoglio, Elena Palczewski, Jan Probability Numerical Analysis 65C30 (Primary), 60H35, 65C20, 46F99 (Secondary) This paper is concerned with numerical solutions of one-dimensional SDEs with the drift being a generalised function, in particular belonging to the Hölder-Zygmund space $C^{-γ}$ of negative order $-γ<0$ in the spatial variable. We design an Euler-Maruyama numerical scheme and prove its convergence, obtaining an upper bound for the strong $L^1$ convergence rate. We finally implement the scheme and discuss the results obtained. |
| title | Convergence rate of numerical scheme for SDEs with a distributional drift in Besov space |
| topic | Probability Numerical Analysis 65C30 (Primary), 60H35, 65C20, 46F99 (Secondary) |
| url | https://arxiv.org/abs/2309.11396 |