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Stochastic Differential Equations versus Fokker-Planck-Kolmogorov Equations: a Short Review and Some Recent Progress

Existence of a strong solution in is proved for the stochastic nonlinear FokkerPlanck equation  , via a corresponding random differential equation. Here d ≥ 1, W is a Wiener process in  and β is a continuous monotonically increasing function satisfying some appropriate polynomial growth conditions. The solution exists for and preserves positivity. If β is locally Lipschitz, the solution is unique, path-wise Lipschitz continuous with respect to initial data in . Stochastic Fokker-Planck equations with nonlinear drift of the form are also considered for Lipschitzian continuous functions . Joint work with Viorel Barbu (Romanian Academy of Sciences, Iasi).