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arXiv · 2103.07165

Transition pathways for a class of high dimensional stochastic dynamical systems with L\'{e}vy noise

Jianyu Hu·Jianyu Chen
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Abstract

This work is devoted to deriving the Onsager-Machlup action functional for a class of stochastic differential equations with (non-Gaussian) L\'{e}vy 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 Poincar\'{e} 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.

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Jianyu Hu, Jianyu Chen. 2021-03-12. Transition pathways for a class of high dimensional stochastic dynamical systems with L\'{e}vy noise. https://doi.org/10.1063/5.0050128

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