Abstract
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.
Key-words
- Viscosity solutions
- dynamic programming
- optimal stochastic control
- Hamilton-Jacobi-Bellman equations
- partial observations
- Zakai's equation
- fully nonlinear second-order equations
- infinite dimensions
- degenerate ellipticity
Work partially supported by US Army contract DASA 45-88-C-009.
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Lions, P.L. (1989). Viscosity solutions of fully nonlinear second order equations and optimal stochastic control in infinite dimensions. Part II: Optimal control of Zakai's equation. In: Da Prato, G., Tubaro, L. (eds) Stochastic Partial Differential Equations and Applications II. Lecture Notes in Mathematics, vol 1390. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083943
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DOI: https://doi.org/10.1007/BFb0083943
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