Under mild growth and local regularity assumptions, the Fokker-Planck equation with rough diffusion and unbounded drift has exactly one measure-valued solution for each starting point, and under extra conditions the solution converges to a stationary distribution.
Anderson,Reverse-time diffusion equation models, Stochastic Process
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Cholesky decomposition and well-posedness of Cauchy problem for Fokker-Planck equations with unbounded coefficients
Under mild growth and local regularity assumptions, the Fokker-Planck equation with rough diffusion and unbounded drift has exactly one measure-valued solution for each starting point, and under extra conditions the solution converges to a stationary distribution.