Finite-dimensional filters with nonlinear drift. III: Duncan-Mortensen-Zakai equation with arbitrary initial condition for the linear filtering system and the Benes filtering system |
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| Authors: | Shing-Tung Yau Yau SS-T |
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| Institution: | Dept. of Math., Harvard Univ., Cambridge, MA, USA; |
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| Abstract: | We consider the Duncan-Mortensen-Zakai (DMZ) equation for the Kalman-Bucy filtering system and Benes filtering system. We show that this equation 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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