A parameter estimation method based on random slow manifolds

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.