Multilevel Picard approximations for McKean-Vlasov stochastic differential equations with nonconstant diffusion
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909918323277824 |
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| author | Neufeld, Ariel Nguyen, Tuan Anh Schmocker, Philipp |
| author_facet | Neufeld, Ariel Nguyen, Tuan Anh Schmocker, Philipp |
| contents | We introduce multilevel Picard (MLP) approximations for McKean--Vlasov stochastic differential equations (SDEs) with nonconstant diffusion coefficient. Under standard Lipschitz assumptions on the coefficients, we show that the MLP algorithm approximates the solution of the SDE in the $L^2$-sense without the curse of dimensionality. The latter means that its computational cost grows at most polynomially in both the dimension and the reciprocal of the prescribed error tolerance. In two numerical experiments, we demonstrate its applicability by approximating McKean--Vlasov SDEs in dimensions up to 1000. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_03205 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multilevel Picard approximations for McKean-Vlasov stochastic differential equations with nonconstant diffusion Neufeld, Ariel Nguyen, Tuan Anh Schmocker, Philipp Numerical Analysis Probability We introduce multilevel Picard (MLP) approximations for McKean--Vlasov stochastic differential equations (SDEs) with nonconstant diffusion coefficient. Under standard Lipschitz assumptions on the coefficients, we show that the MLP algorithm approximates the solution of the SDE in the $L^2$-sense without the curse of dimensionality. The latter means that its computational cost grows at most polynomially in both the dimension and the reciprocal of the prescribed error tolerance. In two numerical experiments, we demonstrate its applicability by approximating McKean--Vlasov SDEs in dimensions up to 1000. |
| title | Multilevel Picard approximations for McKean-Vlasov stochastic differential equations with nonconstant diffusion |
| topic | Numerical Analysis Probability |
| url | https://arxiv.org/abs/2502.03205 |