Convergence rate of Euler-Maruyama scheme for McKean-Vlasov SDEs with density-dependent drift
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912717643710464 |
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| author | Le, Anh-Dung |
| author_facet | Le, Anh-Dung |
| contents | In this paper, we study weak well-posedness of a McKean-Vlasov stochastic differential equations (SDEs) whose drift is density-dependent and whose diffusion is constant. The existence part is due to Hölder stability estimates of the associated Euler-Maruyama scheme. The uniqueness part is due to that of the associated Fokker-Planck equation. We also obtain convergence rate in weighted $L^1$ norm for the Euler-Maruyama scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_19121 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convergence rate of Euler-Maruyama scheme for McKean-Vlasov SDEs with density-dependent drift Le, Anh-Dung Numerical Analysis Probability In this paper, we study weak well-posedness of a McKean-Vlasov stochastic differential equations (SDEs) whose drift is density-dependent and whose diffusion is constant. The existence part is due to Hölder stability estimates of the associated Euler-Maruyama scheme. The uniqueness part is due to that of the associated Fokker-Planck equation. We also obtain convergence rate in weighted $L^1$ norm for the Euler-Maruyama scheme. |
| title | Convergence rate of Euler-Maruyama scheme for McKean-Vlasov SDEs with density-dependent drift |
| topic | Numerical Analysis Probability |
| url | https://arxiv.org/abs/2412.19121 |