Numerical Results of Nonlinear Filtering Problem from Yau-Yau Method

In the paper, we introduce a kind of method to solve the nonlinear filtering problem. Firstly, we review the basic filtering problem and the reduction from robust Duncan-Mortensen-Zakai equation to Kolmogorov equation. Then we use the difference discrete method to solve the Kolmogorov equation. The result is given to prove that the solution of the difference scheme convergences pointwise to the solution of the initial-value problem of the Kolmogorov equation. At last, the numerical results show that the numerical method can give the exact result.