Existence of a strong solution in
![](/uploads/20171013/d8a9233bdecce92f32044907c4576023.png)
is proved for the stochastic nonlinear FokkerPlanck
equation
![](/uploads/20171013/709bcd958bf3df35670b4082d8cd3e05.png)
,
via a corresponding random differential equation. Here d ≥ 1, W is a Wiener process in
![](/uploads/20171013/4a84615b42c0cd3710ca2218b20526fd.png)
and β is a continuous monotonically increasing function satisfying
some appropriate polynomial growth conditions. The solution exists for
![](/uploads/20171013/c7d37655eec0f6da93bd9ae2a3a98c10.png)
and
preserves positivity. If β is locally Lipschitz, the solution is unique, path-wise Lipschitz continuous
with respect to initial data in
![](http://math.sustc.edu.cn/uploads/20171013/09862ea4c731cd30886dc2a939f8303b.png)
. Stochastic Fokker-Planck equations with nonlinear
drift of the form
![](/uploads/20171013/652f19f4e1029ff97ecefc9c74cf7ca8.png)
are also considered for Lipschitzian
continuous functions
![](/uploads/20171013/ab2d8f22cb5b3327497cc32c2cbee212.png)
.
Joint work with Viorel Barbu (Romanian Academy of Sciences, Iasi).