Slow manifold and parameter estimation for a nonlocal fast-slow stochastic evolutionary system

TL;DR

This paper develops a slow manifold theory for a nonlocal fast-slow stochastic system with anomalous diffusion, enabling dimension reduction and parameter estimation based on observable slow components.

Contribution

It introduces a slow manifold for a nonlocal stochastic system with anomalous diffusion and demonstrates its exponential tracking property for effective dimension reduction and parameter estimation.

Findings

Established a slow manifold for the system.

Proved exponential tracking property of the manifold.

Facilitated parameter estimation using reduced system.

Abstract

We establish a slow manifold for a fast-slow stochastic evolutionary system with anomalous diffusion, where both fast and slow components are influ- enced by white noise. Furthermore, we prove the exponential tracking property for the random slow manifold and this leads to a lower dimensional reduced sys- tem based on the slow manifold. Also we consider parameter estimation for this nonlocal fast-slow stochastic dynamical system, where only the slow component is observable. In quantifying parameters in stochastic evolutionary systems, this offers an advantage of dimension reduction.