  A parameter estimation method is devised for a slow-fast stochastic dynamical
system, where often only the slow component is observable. By using the
observations only on the slow component, the system parameters are estimated by
working on the slow system on the random slow manifold. This offers a benefit
of dimension reduction in quantifying parameters in stochastic dynamical
systems. An example is presented to illustrate this method, and verify that the
parameter estimator based on the lower dimensional, reduced slow system is a
good approximation of the parameter estimator for original slow-fast stochastic
dynamical system.
