Viscosity solutions of fully nonlinear second order equations and optimal stochastic control in infinite dimensions. Part II: Optimal control of Zakai's equation

We consider here the value function corresponding to the optimal control of Zakai's equation and we study various regularity properties of this value function in the context of L2 distributions. In particular, we show that it is the unique viscosity solution of the corresponding infinite dimensionnal Hamilton-Jacobi-Bellman equation.

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