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We study a Wong-Zakai approximation for the random slow manifold of aslow-fast stochastic dynamical system. We first deduce the existence of therandom slow manifold about an approximation system driven by an integratedOrnstein-Uhlenbeck (O-U) process. Then we compute the slow manifold of theapproximation system, in order to gain insights of the long time dynamics ofthe original stochastic system. By restricting this approximation system to itsslow manifold, we thus get a reduced slow random system. This reduced slowrandom system is used to accurately estimate a system parameter of the originalsystem. An example is presented to illustrate this approximation.

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