Transition pathways for a class of degenerate stochastic dynamical systems with Lévy noise
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910778246823936 |
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| author | Chao, Ying Wei, Pingyuan |
| author_facet | Chao, Ying Wei, Pingyuan |
| contents | This work is devoted to deriving the Onsager--Machlup function for a class of degenerate stochastic dynamical systems with (non-Gaussian) Lévy noise as well as Brownian noise. This is obtained based on the Girsanov transformation and then by a path representation. Moreover, this Onsager--Machlup function may be regarded as a Lagrangian giving the most probable transition pathways. The Hamilton--Pontryagin principle is essential to handle such a variational problem in degenerate case. Finally, a kinetic Langevin system in which noise is degenerate is specifically investigated analytically and numerically. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_05215 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Transition pathways for a class of degenerate stochastic dynamical systems with Lévy noise Chao, Ying Wei, Pingyuan Dynamical Systems Probability This work is devoted to deriving the Onsager--Machlup function for a class of degenerate stochastic dynamical systems with (non-Gaussian) Lévy noise as well as Brownian noise. This is obtained based on the Girsanov transformation and then by a path representation. Moreover, this Onsager--Machlup function may be regarded as a Lagrangian giving the most probable transition pathways. The Hamilton--Pontryagin principle is essential to handle such a variational problem in degenerate case. Finally, a kinetic Langevin system in which noise is degenerate is specifically investigated analytically and numerically. |
| title | Transition pathways for a class of degenerate stochastic dynamical systems with Lévy noise |
| topic | Dynamical Systems Probability |
| url | https://arxiv.org/abs/2501.05215 |