I was wondering if there are any other means of obtaining exact (or analytical approximations) of the phase space probability density for a system evolving according to Langevin dynamics. The typical approach seems to be to pass to the Fokker-Planck equation corresponding to the underlying Langevin equation and then solve for its steady state. However, for some types of noise (general coloured noise for example) this approach seems to give rise to insurmountable difficulties. I'm not familiar with any other means of getting to the steady-state probability distribution but wondered if there are any out there?
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