PDE, Differential Geometric and Algebraic Methods in Nonlinear Filtering
Stephen S.‐T. Yau · 1993
We have constructed explicitly the most general class of finite dimensional filters which include both Kalman-Bucy filters and Benes filters as special cases. We also proved that if the state space dimension is less than three, then generically all finite dimensional filters must be those constructed by us from the Lie algebraic point of view. Without making any assumption on the drift term of the filtering system, we can write down the asymptotic solution to the famous Kolmogorov equation which is a fundamental equation in Applied Science, Moreover we have an explicit algorithm to construct the convergent solution from this formal asymptotic solution. Nonlinear filtering, Finite dimensional filters, Kolmogorov equation.