Dynamical Inference for Transitions in Stochastic Systems with $\alpha-$stable L\'evy Noise

TL;DR

This paper develops a method to infer transition behaviors in stochastic systems driven by non-Gaussian $$-stable Le9vy noise using nonlocal Zakai equations, applicable to both discrete and continuous observations.

Contribution

It introduces a novel approach for analyzing metastable state transitions in systems with non-Gaussian noise via nonlocal filtering equations.

Findings

Effective inference of transition phenomena demonstrated.

Applicable to both discrete and continuous observation data.

Examples validate the proposed method.

Abstract

A goal of data assimilation is to infer stochastic dynamical behaviors with available observations. We consider transition phenomena between metastable states for a stochastic system with (non-Gaussian) $\alpha-$stable L\'evy noise. With either discrete time or continuous time observations, we infer such transitions by computing the corresponding nonlocal Zakai equation (and its discrete time counterpart) and examining the most probable orbits for the state system. Examples are presented to demonstrate this approach.