Stochastic integral representations for the Ray-Knight theorem of the Levy forest
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909947940306944 |
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| author | Li, Pei-Sen Li, Zenghu Zhang, Wenjing |
| author_facet | Li, Pei-Sen Li, Zenghu Zhang, Wenjing |
| contents | We present a simple stochastic integral representation for the local times of the height process of a spectrally positive Levy process stopped at a hitting time. From the representation we derive a strong stochastic equation for the local time process of the type of Bertoin and Le Gall (Illinois J. Math., 2006) and Dawson and Li (Ann. Probab., 2012). This leads to a representation of the Ray-Knight theorem of Le Gall and Le Jan (Ann. Probab., 1998) and Duquesne and Le Gall (Asterisque, 2002), which codes the genealogical forest of a continuous-state branching process. The results extend those in the recent work of Aidekon et al. (Sci. China Math., 2024) for a Brownian motion with a local time drift. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_06884 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stochastic integral representations for the Ray-Knight theorem of the Levy forest Li, Pei-Sen Li, Zenghu Zhang, Wenjing Probability 60G51, 60J55, 60J80 We present a simple stochastic integral representation for the local times of the height process of a spectrally positive Levy process stopped at a hitting time. From the representation we derive a strong stochastic equation for the local time process of the type of Bertoin and Le Gall (Illinois J. Math., 2006) and Dawson and Li (Ann. Probab., 2012). This leads to a representation of the Ray-Knight theorem of Le Gall and Le Jan (Ann. Probab., 1998) and Duquesne and Le Gall (Asterisque, 2002), which codes the genealogical forest of a continuous-state branching process. The results extend those in the recent work of Aidekon et al. (Sci. China Math., 2024) for a Brownian motion with a local time drift. |
| title | Stochastic integral representations for the Ray-Knight theorem of the Levy forest |
| topic | Probability 60G51, 60J55, 60J80 |
| url | https://arxiv.org/abs/2512.06884 |