Rare events of small-noise Doob conditioned processes
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866913159221084160 |
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| author | Mamede, Iago N. Coghi, Francesco |
| author_facet | Mamede, Iago N. Coghi, Francesco |
| contents | Doob fixed-time conditioning enables the sampling of rare trajectories of Markov processes by modifying the drift so that reaching a prescribed target at a given time is guaranteed. We study the statistics of this conditioned path ensemble through the moment generating function in the weak-noise large deviation regime. Since the Doob drift is rarely available in closed form, we reinterpret the conditioned ensemble as the original process post-selected on the terminal constraint, thereby avoiding explicit construction of the Doob transform. This viewpoint then yields an optimal-control representation for the leading exponential contribution to the generating function, expressed as a variational principle with terminal boundary conditions set by the Doob end-point constraint. We illustrate the framework with two analytical examples and with an application to heat dissipation of a minimal model of biomolecular folding. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_24537 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Rare events of small-noise Doob conditioned processes Mamede, Iago N. Coghi, Francesco Statistical Mechanics Mathematical Physics Probability Doob fixed-time conditioning enables the sampling of rare trajectories of Markov processes by modifying the drift so that reaching a prescribed target at a given time is guaranteed. We study the statistics of this conditioned path ensemble through the moment generating function in the weak-noise large deviation regime. Since the Doob drift is rarely available in closed form, we reinterpret the conditioned ensemble as the original process post-selected on the terminal constraint, thereby avoiding explicit construction of the Doob transform. This viewpoint then yields an optimal-control representation for the leading exponential contribution to the generating function, expressed as a variational principle with terminal boundary conditions set by the Doob end-point constraint. We illustrate the framework with two analytical examples and with an application to heat dissipation of a minimal model of biomolecular folding. |
| title | Rare events of small-noise Doob conditioned processes |
| topic | Statistical Mechanics Mathematical Physics Probability |
| url | https://arxiv.org/abs/2605.24537 |