Transition pathways for a class of high dimensional stochastic dynamical systems with Lévy noise
1School of Mathematics and Statistics and Center for Mathematical Sciences and Hubei National Center for Applied Mathematics, Huazhong University of Science and Technology, Wuhan 430074, China.
Abstract:
This work is devoted to deriving the Onsager-Machlup action functional for a class of stochastic differential equations with (non-Gaussian) Lévy process as well as Brownian motion in high dimensions. This is achieved by applying the Girsanov transformation for probability measures and then by a path representation. The Poincaré lemma is essential to handle such a path representation problem in high dimensions. We provide a sufficient condition on the vector field such that this path representation holds in high dimensions. Moreover, this Onsager-Machlup action functional may be considered as the integral of a Lagrangian. Finally, by a variational principle, we investigate the most probable transition pathways analytically and numerically.
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