  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 (O-U) 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.
