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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    Title :

    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


    Contributors:


    Publication date :

    1997-10-01


    Size :

    1320721 byte




    Type of media :

    Article (Journal)


    Type of material :

    Electronic Resource


    Language :

    English