Optimal Fluctuations for Discrete-time Markov Jump Processes
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918377855909888 |
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| author | Zhao, Feng Zhu, Jinjie Li, Yang Liu, Xianbin Jin, Dongping |
| author_facet | Zhao, Feng Zhu, Jinjie Li, Yang Liu, Xianbin Jin, Dongping |
| contents | In the last few decades, noise-induced large fluctuations and transition phenomena have garnered significant attention in a variety of scientific contexts. The concept of prehistory probability has been proposed within the framework of Langevin dynamics to illustrate the focusing effect of large fluctuation paths onto a deterministic trajectory known as the optimal path. The present paper is devoted to showing that such a focusing effect persists within the framework of discrete-time Markov jump processes. Our proof leverages large deviation theory and the concept of time reversal for Markov jump processes. A key finding is the relationship identified between the optimal path and the time reversal of a specific family of probability distributions. This theoretical framework elucidates how an essentially deterministic mechanism can emerge from rare stochastic events in discrete-time Markov jump systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_06815 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Optimal Fluctuations for Discrete-time Markov Jump Processes Zhao, Feng Zhu, Jinjie Li, Yang Liu, Xianbin Jin, Dongping Probability In the last few decades, noise-induced large fluctuations and transition phenomena have garnered significant attention in a variety of scientific contexts. The concept of prehistory probability has been proposed within the framework of Langevin dynamics to illustrate the focusing effect of large fluctuation paths onto a deterministic trajectory known as the optimal path. The present paper is devoted to showing that such a focusing effect persists within the framework of discrete-time Markov jump processes. Our proof leverages large deviation theory and the concept of time reversal for Markov jump processes. A key finding is the relationship identified between the optimal path and the time reversal of a specific family of probability distributions. This theoretical framework elucidates how an essentially deterministic mechanism can emerge from rare stochastic events in discrete-time Markov jump systems. |
| title | Optimal Fluctuations for Discrete-time Markov Jump Processes |
| topic | Probability |
| url | https://arxiv.org/abs/2603.06815 |