Data-driven approximation of transfer operators for mean-field stochastic differential equations

Eirini Ioannou, Stefan Klus, Gonçalo dos Reis

correctmedium confidence

Category: math.DS
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:57 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper proves L2 convergence of K̂NM^⊤ to CNGN^{-1} (as M→∞, h→0) and almost-sure convergence to (CN+E(h))GN^{-1} for fixed h with E(h)→0, using LLN, bounded/Lipschitz bases, and continuity of inversion; the model reproduces the same argument with a slightly more explicit matrix-perturbation bound and a three-term decomposition. Conclusions and required assumptions match.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The paper establishes EDMD convergence results tailored to decoupled McKean–Vlasov SDEs under natural assumptions. The arguments are correct and closely follow standard techniques (LLN, bounded/Lipschitz bases, Euler/decoupling error control, continuity of inversion). One technical step—L2 convergence of the inverse of the Gram estimator—could be made explicit via a standard resolvent bound to improve clarity. With that minor clarification, the presentation is solid and of interest to specialists.