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Abstract. Optimal control problems governed by semilinear parabolic partial differential equations are considered. No Cesari-type conditions are assumed. By proving the existence theorem and the Pontryagin maximum principle of optimal ``state-control" pairs for the corresponding relaxed...
Abstract. We derive a large deviation principle for the optimal filter where the signal and the observation processes take values in conuclear spaces. The approach follows from the framework established by the author in an earlier paper. The key is the verification of the exponential tightness...
Abstract. An approximation to the solution of a stochastic parabolic equation is constructed using the Galerkin approximation followed by the Wiener chaos decomposition. The result is applied to the nonlinear filtering problem for the time-homogeneous diffusion model with correlated noise. An...
Abstract. This work is concerned with Carleman inequalities and controllability properties for the following stochastic linear heat equation (with Dirichlet boundary conditions in the bounded domain D
and multiplicative noise):
Abstract. In this paper we give a new proof of the existence result of Bensoussan [1, Theorem II-6.1] for the Bellman equation of ergodic control with periodic structure. This Bellman equation is a nonlinear PDE, and he constructed its solution by using the solution of a nonlinear PDE. On the...
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