On modified Euler methods for McKean-Vlasov stochastic differential equations with super-linear coefficients
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915142277529600 |
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| author | Jian, Jiamin Song, Qingshuo Wang, Xiaojie Zhang, Zhongqiang Zhao, Yuying |
| author_facet | Jian, Jiamin Song, Qingshuo Wang, Xiaojie Zhang, Zhongqiang Zhao, Yuying |
| contents | We introduce a new class of numerical methods for solving McKean-Vlasov stochastic differential equations, which are relevant in the context of distribution-dependent or mean-field models, under super-linear growth conditions for both the drift and diffusion coefficients. Under certain non-globally Lipschitz conditions, the proposed numerical approaches have half-order convergence in the strong sense to the corresponding system of interacting particles associated with McKean-Vlasov SDEs. By leveraging a result on the propagation of chaos, we establish the full convergence rate of the modified Euler approximations to the solution of the McKean-Vlasov SDEs. Numerical experiments are included to validate the theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_05057 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On modified Euler methods for McKean-Vlasov stochastic differential equations with super-linear coefficients Jian, Jiamin Song, Qingshuo Wang, Xiaojie Zhang, Zhongqiang Zhao, Yuying Numerical Analysis 65C30 We introduce a new class of numerical methods for solving McKean-Vlasov stochastic differential equations, which are relevant in the context of distribution-dependent or mean-field models, under super-linear growth conditions for both the drift and diffusion coefficients. Under certain non-globally Lipschitz conditions, the proposed numerical approaches have half-order convergence in the strong sense to the corresponding system of interacting particles associated with McKean-Vlasov SDEs. By leveraging a result on the propagation of chaos, we establish the full convergence rate of the modified Euler approximations to the solution of the McKean-Vlasov SDEs. Numerical experiments are included to validate the theoretical results. |
| title | On modified Euler methods for McKean-Vlasov stochastic differential equations with super-linear coefficients |
| topic | Numerical Analysis 65C30 |
| url | https://arxiv.org/abs/2502.05057 |