Nonlinear weak error expansion of McKean-Vlasov stochastic differential equations
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914170851557376 |
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| author | Jourdain, Benjamin Le, Anh-Dung |
| author_facet | Jourdain, Benjamin Le, Anh-Dung |
| contents | According to Talay and Tubaro \cite{talay_expansion_1990}, the weak error between the solution to a stochastic differential equation with smooth coefficients and its Euler-Maruyama scheme can be expanded in powers of the time-step. In the present paper, we generalize this result to the case when the error is measured by a smooth functional on the Wasserstein space of probability measures in place of the linear functional given by the expectation of a smooth function considered in \cite{talay_expansion_1990}. Since this does not complicate our analysis based on the master partial differential equation, we even deal with the McKean-Vlasov case when the coefficients of the stochastic differential equation may depend on its current marginal distribution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_20389 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonlinear weak error expansion of McKean-Vlasov stochastic differential equations Jourdain, Benjamin Le, Anh-Dung Probability 60H10, 60H35 According to Talay and Tubaro \cite{talay_expansion_1990}, the weak error between the solution to a stochastic differential equation with smooth coefficients and its Euler-Maruyama scheme can be expanded in powers of the time-step. In the present paper, we generalize this result to the case when the error is measured by a smooth functional on the Wasserstein space of probability measures in place of the linear functional given by the expectation of a smooth function considered in \cite{talay_expansion_1990}. Since this does not complicate our analysis based on the master partial differential equation, we even deal with the McKean-Vlasov case when the coefficients of the stochastic differential equation may depend on its current marginal distribution. |
| title | Nonlinear weak error expansion of McKean-Vlasov stochastic differential equations |
| topic | Probability 60H10, 60H35 |
| url | https://arxiv.org/abs/2511.20389 |