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arXiv · 2502.05057

On modified Euler methods for McKean-Vlasov stochastic differential equations with super-linear coefficients

Jiamin Jian·Qingshuo Song·Xiaojie Wang·Zhongqiang Zhang·Yuying Zhao
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Abstract

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.

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Jiamin Jian, Qingshuo Song, Xiaojie Wang, Zhongqiang Zhang, Yuying Zhao. 2025-02-07. On modified Euler methods for McKean-Vlasov stochastic differential equations with super-linear coefficients. https://arxiv.org/abs/2502.05057

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