Nonlinear weak error expansion of McKean-Vlasov stochastic differential equations
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.
Keywords
Cite
@article{arxiv.2511.20389,
title = {Nonlinear weak error expansion of McKean-Vlasov stochastic differential equations},
author = {Benjamin Jourdain and Anh-Dung Le},
journal= {arXiv preprint arXiv:2511.20389},
year = {2025}
}