Characterization of the Most Probable Transition Paths of Stochastic Dynamical Systems with Stable Lévy Noise

Abstract

This work is devoted to the investigation of the most probable transition path for stochastic dynamical systems driven by either symmetric $\alpha$-stable Lévy motion ($0<\alpha <1$) or Brownian motion. For stochastic dynamical systems with Brownian motion, minimizing an action functional is a general method to determine the most probable transition path. We have developed a method based on path integrals to obtain the most probable transition path of stochastic dynamical systems with symmetric $\alpha$-stable Lévy motion or Brownian motion, and the most probable path can be characterized by a deterministic dynamical system.