Despite its usefulness, the Kalman-Bucy filter is not perfect. One of its weaknesses is that it needs a Gaussian assumption on the initial data. Recently Yau and Yau introduced a new direct method to solve the estimation problem for linear filtering with non-Gaussian initial data. They factored the problem into two parts: (1) the on-line solution of a finite system of ordinary differential equations (ODEs), and (2) the off-line calculation of the Kolmogorov equation. Here we derive an explicit closed-form solution of the Kolmogorov equation. We also give some properties and conduct a numerical study of the solution.


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    Title :

    Finite-dimensional filters with nonlinear drift. V: solution to Kolmogorov equation arising from linear filtering with non-Gaussian initial condition


    Contributors:
    Zhigang Liang, (author) / Yau, S.S.-T. (author) / Yau, S.T. (author)


    Publication date :

    1997-10-01


    Size :

    1868337 byte




    Type of media :

    Article (Journal)


    Type of material :

    Electronic Resource


    Language :

    English