# Characterization of the Most Probable Transition Paths of Stochastic Dynamical Systems with Stable L\'{e}vy Noise

## TL;DR

This paper develops a unified path integral method to characterize the most probable transition paths in stochastic dynamical systems driven by symmetric alpha-stable Lévy noise or Brownian motion, linking stochastic paths to deterministic systems.

## Contribution

It introduces a novel path integral approach to determine the most probable transition paths for systems with Lévy noise, extending existing methods for Brownian motion.

## Key findings

- Unified framework for Lévy and Brownian systems
- Most probable paths characterized by deterministic systems
- Applicable to a range of stochastic dynamical systems

## Abstract

This work is devoted to the investigation of the most probable transition path for stochastic dynamical systems driven by either symmetric $\alpha$-stable L\'{e}vy 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 L\'{e}vy motion or Brownian motion, and the most probable path can be characterized by a deterministic dynamical system.