Randomised one-step time integration methods for deterministic operator differential equations

Han Cheng Lie, Martin Stahn, T. J. Sullivan

correctmedium confidence

Category: math.DS
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The candidate solution proves the same pathwise and expected error bounds as Theorem 2.6 in the paper, but via a different weighting/Jensen step instead of the paper’s Lemma B.4 inequality. The paper’s assumptions (Lipschitz Φ, uniform local truncation, (p,R)-regular noise) are the same as those used in the candidate solution, and the final bounds match the stated forms (up to harmless constant choices). Minor differences include the explicit use of h* ≤ 1 in the paper and an implicit reliance on h ≤ 1 in the candidate’s constant estimates. Overall, both arguments are logically sound and yield the same results .

Referee report (LaTeX)

\textbf{Recommendation:} no revision

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The paper’s main theorems are correct and clearly proved. They extend known finite-dimensional, uniform-grid results to Banach and variational settings with non-uniform grids, and the assumptions are well-motivated. The candidate solution provides a complementary proof that reaches the same bounds, reinforcing the correctness of the results. Minor presentation improvements could further streamline the exposition.