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New preprint! A Complete Decomposition of Stochastic Differential Equations I characterise *all possible SDEs* that satisfy given time-dependent marginals p(x,t)

Here is the decomposition: I show that the scalar ϕ is unique(!) but you can choose and Q or D. In diffusion the ϕ terms represent the "probability flow ODE" but there are actually many ODEs which satisfy p(x,t) depending on your choice of Q