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).