Neural CDEs for Long Time Series via the Log-ODE Method

The paper states the local log-ODE error (Eq. 29) and derives the global partition-wise error (Theorem B.7, Eq. 34) by citing Gyurkó’s thesis; the candidate solution proves the same bound via Bailleul’s C^1-approximate flows and a non-commutative sewing lemma. The statements, hypotheses (X geometric p-rough, f ∈ Lip(γ), γ > p), and the smallness condition on max_i ||X||_{p-var;[t_i,t_{i+1}]} all match the paper’s setup, and the final inequality coincides with Theorem B.7. Thus both are correct and reach the same result by different routes .