A new stochastic framework for ship capsizing

The paper explicitly states the committor-based identity for the density of reactive trajectories ρ_R(x) = q+(x) ρ(x) q−(x) and frames capsize time as the first intersection with a dividing manifold whose distribution function’s derivative is the (unconditional) capsize rate, and it notes that filtered-white-noise forcing makes the augmented state (x,z) Markovian . The candidate solution gives standard measure-theoretic justifications of these claims (factorization via Markov property, stopping-time via Debut theorem) and clarifies regularity assumptions. Thus, the paper’s statements are correct at a high level, and the model’s solution provides a compatible, more rigorous proof sketch. Minor clarifications (e.g., differentiability of F for r(t)=F′(t), measurability/boundary conditions for committors) would strengthen the paper.