  This work is devoted to deriving the Onsager-Machlup function for a class of
stochastic dynamical systems under (non-Gaussian) Levy noise as well as
(Gaussian) Brownian noise, and examining the corresponding most probable paths.
This Onsager-Machlup function is the Lagrangian giving the most probable path
connecting metastable states for jump-diffusion processes. This is done by
applying the Girsanov transformation for measures induced by jump-diffusion
processes. Moreover, we have found this Lagrangian function is consistent with
the result in the special case of diffusion processes. Finally, we apply this
new Onsager-Machlup function to investigate dynamical behaviors analytically
and numerically in several examples. These include the transitions from one
metastable state to another metastable state in a double-well system, with
numerical experiments illustrating most probable transition paths for various
noise parameters.
