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

In this note, we consider the explicit solution of Duncan-Mortensen-Zakai ( DMZ) equation for the finite-dimensional filtering system. We show that Yau filtering system ((partial derivativef(j)/partial derivativex(i)) - (parti al derivativef(i)/partial derivativex(j)) = c(ij) = 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. L et n be the dimension of state space. We show that we need only n sufficien t statistics in order to solve the DMZ equation.