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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.12717 |
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| _version_ | 1866910705405394944 |
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| author | Riera, Armand Rosales-Ortiz, Alejandro |
| author_facet | Riera, Armand Rosales-Ortiz, Alejandro |
| contents | We develop an excursion theory that describes the evolution of a Markov process indexed by a Levy tree away from a regular and instantaneous point $x$ of the state space. The theory builds upon a notion of local time at $x$ that was recently introduced in [37]. Despite the radically different setting, our results exhibit striking similarities to the classical excursion theory for $\mathbb{R}_+$-indexed Markov processes. We then show that the genealogy of the excursions can be encoded in a Levy tree called the tree coded by the local time. In particular, we recover by different methods the excursion theory of Abraham and Le Gall [2], which was developed for Brownian motion indexed by the Brownian tree. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_12717 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Excursion theory for Markov processes indexed by Levy trees Riera, Armand Rosales-Ortiz, Alejandro Probability We develop an excursion theory that describes the evolution of a Markov process indexed by a Levy tree away from a regular and instantaneous point $x$ of the state space. The theory builds upon a notion of local time at $x$ that was recently introduced in [37]. Despite the radically different setting, our results exhibit striking similarities to the classical excursion theory for $\mathbb{R}_+$-indexed Markov processes. We then show that the genealogy of the excursions can be encoded in a Levy tree called the tree coded by the local time. In particular, we recover by different methods the excursion theory of Abraham and Le Gall [2], which was developed for Brownian motion indexed by the Brownian tree. |
| title | Excursion theory for Markov processes indexed by Levy trees |
| topic | Probability |
| url | https://arxiv.org/abs/2411.12717 |