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