General Mathematics

A Sharp Uniform-in-Time Wasserstein-1 Bound for Stochastic Runge—Kutta Integrators of Langevin Dynamics

Authors: Yuliang Wang, Xuda Ye

We consider two stochastic Runge--Kutta integrators proposed by Yang & Wang (2026) for overdamped Langevin dynamics whose potential is strongly convex outside a bounded region. In the companion paper (Ye, 2026) the law of the numerical solution was shown to approach the law of the exact solution at second order in Wasserstein-1 distance, uniformly in the number of steps, up to a logarithm of the step size. We remove the logarithm, and a Gaussian example shows that the second order is attained by the bias of the invariant law of the integrators, and that the squared bias of their time averages attains the order $h^4$ of the mean square error bound of the companion paper.

Comments: 23 Pages.

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Submission history

[v1] 2026-09-22 15:22:47

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