Transition pathways for a class of high dimensional stochastic dynamical systems with Lévy noise
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2021
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| Acceso en línea: | |
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| _version_ | 1866911922660573184 |
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| author | Hu, Jianyu Chen, Jianyu |
| author_facet | Hu, Jianyu Chen, Jianyu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_07165 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Transition pathways for a class of high dimensional stochastic dynamical systems with Lévy noise Hu, Jianyu Chen, Jianyu Dynamical Systems Probability 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. |
| title | Transition pathways for a class of high dimensional stochastic dynamical systems with Lévy noise |
| topic | Dynamical Systems Probability |
| url | https://arxiv.org/abs/2103.07165 |