2404.10698
Drift estimation in stochastic flows using kernel integral operators
Suddhasattwa Das
wrongmedium confidenceCounterexample detected
- Category
- math.DS
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
Two central identities in the paper are misstated: (i) the paper claims V = E_μ(proj2 | proj1) (its Eq. (8)), but with μ’s second coordinate taken to be X(t+Δt) this is dimensionally incorrect unless one takes a short-time limit or uses increments; (ii) the paper’s third-order drift identity (its Eq. (5)) is off by a factor of 6 on the left-hand side. The candidate solution diagnoses and corrects both, and its RKHS-consistency argument matches the paper’s Lemma 2.1 and algorithmic setup.
Referee report (LaTeX)
\textbf{Recommendation:} major revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The paper's core idea—estimating drift via conditional expectations and kernel integral operators—is valuable and practically relevant. However, two centerpiece equations are misstated. Equation (8) equating V to a conditional expectation of the next state is dimensionally wrong without a short-time limit or increment normalization, and Equation (5) omits a factor of six. These propagate into Algorithm 2’s target. With these corrected and assumptions clarified, the contribution would be solid and publishable.