Effective filtering analysis for non-Gaussian dynamic systems

TL;DR

This paper investigates a slow-fast data assimilation system with non-Gaussian noise, establishing a low-dimensional reduction via a random invariant manifold and demonstrating the approximation quality of the reduced filter.

Contribution

It introduces a novel analysis of non-Gaussian stochastic systems, proving the existence of a random invariant manifold and its use for effective filter approximation.

Findings

Existence of a random invariant manifold for non-Gaussian systems

Low-dimensional reduction accurately approximates the original filter

Probabilistic bounds on filter approximation quality

Abstract

This work is about a slow-fast data assimilation system under non-Gaussian noisy fluctuations. Firstly, we show the existence of a random invariant manifold for a stochastic dynamical system with non-Gaussian noise and two-time scales. Secondly, we obtain a low dimensional reduction of this system via a random invariant manifold. Thirdly, we prove that the low dimensional filter on the random invariant manifold approximates the original filter, in a probabilistic sense.