Explicit numerical approximations for McKean-Vlasov stochastic differential equations in finite and infinite time
Abstract
Inspired by the stochastic particle method, this paper establishes an easily implementable explicit numerical method for McKean-Vlasov stochastic differential equations (MV-SDEs) with superlinear growth coefficients. The paper establishes the theory on the propagation of chaos in the Lq sense. The optimal uniform-in-time strong convergence rate 1/2-order of the numerical solutions is obtained for the interacting particle system. Furthermore, it is proved that the numerical solutions capture the long-term dynamical behaviors of MV-SDEs precisely, including moment boundedness, stability, and ergodicity. Moreover, a unique numerical invariant probability measure is yielded, which converges to the underlying invariant probability measure of MV-SDEs in the L2-Wasserstein distance. Finally, several numerical experiments are carried out to support the main results.
Keywords
Cite
@article{arxiv.2401.02878,
title = {Explicit numerical approximations for McKean-Vlasov stochastic differential equations in finite and infinite time},
author = {Yuanping Cui and Xiaoyue Li and Yi Liu and Fengyu Wang},
journal= {arXiv preprint arXiv:2401.02878},
year = {2025}
}