Effective Filtering for Multiscale Stochastic Dynamical Systems in Hilbert Spaces

TL;DR

This paper develops an effective filtering approach for slow-fast stochastic systems in Hilbert spaces by reducing the system to a random invariant manifold and approximating the nonlinear filter, with practical application demonstrated.

Contribution

It introduces a novel reduction technique for filtering in infinite-dimensional stochastic systems and demonstrates its effectiveness through an example.

Findings

Successful reduction to a random invariant manifold

Approximation of nonlinear filtering via reduced system

Application to a practical example confirms effectiveness

Abstract

In the paper, effective filtering for a type of slow-fast data assimilation systems in Hilbert spaces is considered. Firstly, the system is reduced to a system on a random invariant manifold. Secondly, nonlinear filtering of the origin system can be approximated by that of the reduction system. Finally, we apply the obtained result to an example.