Nonlinear weak error expansion of McKean-Vlasov stochastic differential equations

Benjamin Jourdain; Anh-Dung Le

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arXiv · 2511.20389

Nonlinear weak error expansion of McKean-Vlasov stochastic differential equations

Benjamin Jourdain·Anh-Dung Le

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Abstract

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.

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Benjamin Jourdain, Anh-Dung Le. 2025-11-25. Nonlinear weak error expansion of McKean-Vlasov stochastic differential equations. https://arxiv.org/abs/2511.20389

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