Key points are not available for this paper at this time.
It is shown that if a diffusion process, \Xₜ: 0 t 1\, on Rᵈ satisfies dXₜ = b (t, Xₜ) dt + (t, Xₜ) dwₜ then the reversed process, \Xₜ: 0 t 1\ where Xₜ = X₁ - ₓ, is again a diffusion with drift b and diffusion coefficient, provided some mild conditions on b, , and p₀, the density of the law of X₀, hold. Moreover b and are identified.
Haussmann et al. (Wed,) studied this question.