A systematic path to non-Markovian dynamics II: Probabilistic response of nonlinear multidimensional systems to Gaussian colored noise excitation

Both the paper and the model derive the same closed, nonlinear, nonlocal-in-time pdf-evolution equation (their eq. (2.6)) with diffusion coefficients as in eqs. (5.19a,b). Steps up to the transformed SLE agree exactly (delta-projection + extended Novikov–Furutsu + variational equations). The only discrepancy is that the paper explicitly introduces a Magnus/current-time approximation to obtain G(t;s) and hence the exp(Δ(x,t)(t−s))Φ[R](t;s) factor, while the model presents this “final-time freezing” as if it were exact. Thus, results match and the proof structure is substantially the same, but the model omits to flag the key approximation underpinning the closure. See the paper’s derivation around eqs. (3.5), (3.16), (5.15)–(5.19) .