The authors construct a Mortensen-type observer on the Wasserstein space P2(R^d), establish dynamic programming and viscosity solution properties for the associated HJB equation using two formulations, prove uniqueness via comparison, and introduce a convergent semi-Lagrangian scheme.
Nonlinear filtering and large deviations:a pde-control theoretic approach
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The Mortensen observer on the space of probability measures
The authors construct a Mortensen-type observer on the Wasserstein space P2(R^d), establish dynamic programming and viscosity solution properties for the associated HJB equation using two formulations, prove uniqueness via comparison, and introduce a convergent semi-Lagrangian scheme.