Abstract
Let $\nu$ denote the value function of a partially observed control problem. If $\nu$ is once differentiable in a certain direction $\hat{B}$, then optimal controls are characterized by a feedback involving the directional derivative $\hat{B}\nu$. It is also shown that $\nu$ satisfies the corresponding Bellman equation, an infinite-dimensional PDE on the space of measures, in the viscosity sense of Crandall and Lions.
Citation
Omar Hijab. "Partially Observed Control of Markov Processes. III." Ann. Probab. 18 (3) 1099 - 1125, July, 1990. https://doi.org/10.1214/aop/1176990737
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