Effective filtering for slow-fast systems via wong-zakai approximation

Nonlinear filtering problem has been widely investigated in diverse fields. One important topic related to it is how to formulate an effective approximation scheme for a given observation. By using Wong-Zakai approximation and random invariant manifold theory, we will propose an effective approximation result for a class of slow-fast systems with respect to filtering. We will firstly establish the smooth reduced system via random invariant manifold theory, and then show exponential attractive property of it. At last, we will prove the filtering of the smooth reduced system can well approximate that of the original system.