A Wong–Zakai Approximation for Random Slow Manifolds with Application to Parameter Estimation

We study a Wong–Zakai approximation for the random slow manifold of a slow–fast stochastic dynamical system. We first deduce the existence of the random slow manifold about an approximation system driven by an integrated Ornstein–Uhlenbeck process. Then, we compute the slow manifold of the approximation system, in order to gain insights of the long time dynamics of the original stochastic system. By restricting this approximation system to its slow manifold, we thus get a reduced slow random system. This reduced slow random system is used to accurately estimate a system parameter of the original system. An example is presented to illustrate this approximation.