Data assimilation and parameter estimation for a multiscale stochastic system with alpha-stable Levy noise

TL;DR

This paper develops a stochastic averaging approach for data assimilation in multiscale systems with alpha-stable Levy noise, enabling low-dimensional filtering and parameter estimation when observations are limited to slow components.

Contribution

It introduces a novel averaging method for non-Gaussian Levy noise in multiscale systems, improving filtering and parameter estimation accuracy with reduced computational complexity.

Findings

The averaged filter closely approximates the original filter.

The low-dimensional slow system accurately captures the slow dynamics.

The approach effectively handles non-Gaussian Levy noise in data assimilation.

Abstract

This work is about low dimensional reduction for a slow-fast data assimilation system with non-Gaussian $\alpha-$stable L\'evy noise via stochastic averaging. When the observations are only available for slow components, we show that the averaged, low dimensional filter approximates the original filter, by examining the corresponding Zakai stochastic partial differential equations. Furthermore, we demonstrate that the low dimensional slow system approximates the slow dynamics of the original system, by examining parameter estimation and most probable paths.