Transition pathways for a class of high dimensional stochastic dynamical systems with Lévy noise

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 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.

arXiv commentarXiv admin note: text overlap with arXiv:2011.09690

References in corpus (5)

• A Scaling Theory of Bifurcations in the Symmetric Weak-Noise Escape Problem
• The Onsager-Machlup Function as Lagrangian for the Most Probable Path of a Jump-diffusion Process
• Convergence analysis of a finite element approximation of minimum action methods
• Stochastic analysis in a tubular neighborhood or Onsager-Machlup functions revisited
• Onsager-Machlup action functional for stochastic partial differential equations with Levy noise

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