Transition Path Theory For Lévy-Type Processes: SDE Representation and Statistics
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909005403652096 |
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| author | Huang, Yuanfei Zhou, Xiang |
| author_facet | Huang, Yuanfei Zhou, Xiang |
| contents | This paper establishes a Transition Path Theory (TPT) for Lévy-type processes, addressing a critical gap in the study of the transition mechanism between meta-stabile states in non-Gaussian stochastic systems. A key contribution is the rigorous derivation of the stochastic differential equation (SDE) representation for transition path processes, which share the same distributional properties as transition trajectories, along with a proof of its well-posedness. This result provides a solid theoretical foundation for sampling transition trajectories. The paper also investigates the statistical properties of transition trajectories, including their probability distribution, probability current, and rate of occurrence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_09462 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Transition Path Theory For Lévy-Type Processes: SDE Representation and Statistics Huang, Yuanfei Zhou, Xiang Probability Mathematical Physics This paper establishes a Transition Path Theory (TPT) for Lévy-type processes, addressing a critical gap in the study of the transition mechanism between meta-stabile states in non-Gaussian stochastic systems. A key contribution is the rigorous derivation of the stochastic differential equation (SDE) representation for transition path processes, which share the same distributional properties as transition trajectories, along with a proof of its well-posedness. This result provides a solid theoretical foundation for sampling transition trajectories. The paper also investigates the statistical properties of transition trajectories, including their probability distribution, probability current, and rate of occurrence. |
| title | Transition Path Theory For Lévy-Type Processes: SDE Representation and Statistics |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2506.09462 |