Dynamical inference for transitions in stochastic systems with α-stable Lévy noise

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) α;-stable Lévy noise. With either discrete time or continuous time observations, we infer such transitions between metastable states by computing the corresponding non-local Zakai equation (and its discrete time counterpart) and examining the most probable orbits for the state system. Examples are presented to demonstrate this approach.