Randomized filtering and Bellman equation in Wasserstein space for partial observation control problem
Articolo
Data di Pubblicazione:
2019
Citazione:
Randomized filtering and Bellman equation in Wasserstein space for partial observation control problem / E. Bandini, A. Cosso, M. Fuhrman, H. Pham. - In: STOCHASTIC PROCESSES AND THEIR APPLICATIONS. - ISSN 0304-4149. - 129:2(2019 Feb), pp. 674-711.
Abstract:
We study a stochastic optimal control problem for a partially observed diffusion. By using the
control randomization method in Bandini et al. (2018), we prove a corresponding randomized dynamic
programming principle (DPP) for the value function, which is obtained from a flow property of an associated
filter process. This DPP is the key step towards our main result: a characterization of the value function
of the partial observation control problem as the unique viscosity solution to the corresponding dynamic
programming Hamilton–Jacobi–Bellman (HJB) equation. The latter is formulated as a new, fully non linear
partial differential equation on the Wasserstein space of probability measures. An important feature of
our approach is that it does not require any non-degeneracy condition on the diffusion coefficient, and no
condition is imposed to guarantee existence of a density for the filter process solution to the controlled
Zakai equation. Finally, we give an explicit solution to our HJB equation in the case of a partially observed
non Gaussian linear–quadratic model.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Partial observation control problem; Randomization of controls; Dynamic programming principle; Bellman
equation; Wasserstein space; Viscosity solutions
Elenco autori:
E. Bandini, A. Cosso, M. Fuhrman, H. Pham
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