A parameter estimation method based on random slow manifolds

TL;DR

This paper introduces a parameter estimation technique for slow-fast stochastic systems that leverages random slow manifolds to reduce dimensionality, enabling effective parameter inference from limited observations.

Contribution

It presents a novel method for parameter estimation using the reduced slow system on the random slow manifold, improving efficiency and accuracy in stochastic dynamical systems.

Findings

The estimator based on the reduced slow system closely approximates the original system's parameters.

Dimension reduction via the random slow manifold simplifies the estimation process.

Numerical example confirms the effectiveness of the proposed method.

Abstract

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.