Abstract
This work is devoted to the investigation of the most probable transition paths for stochastic dynamical systems with either symmetric -stable Lévy motion 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 either symmetric -stable Lévy motion () or Brownian motion. Furthermore, we have shown that the most probable path can be characterized by a deterministic dynamical system.
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