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Finite-dimensional filters with nonlinear drift X: explicit solution of DMZ equation

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2 Author(s)
Yan, S.S.-T. ; Dept. of Math. Stat. & Comput. Sci., Illinois Univ., Chicago, IL, USA ; Guo-Qing Hu

In this note, we consider the explicit solution of Duncan-Mortensen-Zakai (DMZ) equation for the finite-dimensional filtering system. We show that Yau's (1990, 1994) filtering system (δfj/δxi)-(δfi /δxi)=cij=constant for all (i,j) can be solved explicitly with an arbitrary initial condition by solving a system of ordinary differential equations and a Kolmogorov-type equation. Let n be the dimension of state space. We show that we need only n sufficient statistics in order to solve the DMZ equation

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Automatic Control, IEEE Transactions on  (Volume:46 ,  Issue: 1 )