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Stein's Method for Convergence Rates of Invariant Measures in the Nonlocal-to-Local Limit
Mingyan Wu, Guohuan Zhao · 2026-05-30 · via math updates on arXiv.org

We utilize Stein's method to establish quantitative bounds on the total variation distance between the invariant measure of a drifted nonlocal Markov operator and that of its local counterpart under minimal assumptions on the drifts. The main ingredient is a reduction via Stein's method that transforms the original problem into analyzing growth estimates for solutions to a nonlocal Poisson equation and decay estimates for the invariant measure of the local operator.

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