A parameter estimation method based on random slow manifolds

A parameter estimation method is devised for a slow–fast stochastic dynamical system, where only the slow component is observable. By using available observations on the slow component, a system parameter is estimated by studying 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 to verify that the parameter estimator based on the lower dimensional, reduced slow system is a good approximation of the parameter estimator for the original slow–fast stochastic dynamical system.