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math.PR2017
Nonlinear Fokker-Planck equations driven by Gaussian linear multiplicative noise
Viorel Barbu, Michael Röckner
Existence and uniqueness of a strong solution in is proved for the stochastic nonlinear Fokker-Planck equation $$dX-{\rm div}(DX)dt-Δβ(X)dt=X\,dW \mbox{ in }(…
math.PR2017
Mild solutions to the dynamic programming equation for stochastic optimal control problems
Viorel Barbu, Chiara Benazzoli, Luca Di Persio
We show via the nonlinear semigroup theory in that the -D dynamic programming equation associated with a stochastic optimal control problem with multiplicative…