Regenerative processes for Poisson zero polytopes
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2017
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| Acceso en línea: | |
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| _version_ | 1866909989009883136 |
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| author | Martínez, Servet Nagel, Werner |
| author_facet | Martínez, Servet Nagel, Werner |
| contents | Let $(M_t: t > 0)$ be a Markov process of tessellations of ${\mathbb R}^\ell$ and $({\cal C}_t:\, t > 0)$ the process of their zero cells (zero polytopes) which has the same distribution as the corresponding process for Poisson hyperplane tessellations. Let $a>1$. Here we describe the stationary zero cell process $(a^t {\cal C}_{a^t}:\, t\in {\mathbb R})$ in terms of some regenerative structure and we prove that it is a Bernoulli flow. An important application are the STIT tessellation processes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1708_08592 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Regenerative processes for Poisson zero polytopes Martínez, Servet Nagel, Werner Probability 60D05, 60J25, 60J75, 37A25, 37A35 Let $(M_t: t > 0)$ be a Markov process of tessellations of ${\mathbb R}^\ell$ and $({\cal C}_t:\, t > 0)$ the process of their zero cells (zero polytopes) which has the same distribution as the corresponding process for Poisson hyperplane tessellations. Let $a>1$. Here we describe the stationary zero cell process $(a^t {\cal C}_{a^t}:\, t\in {\mathbb R})$ in terms of some regenerative structure and we prove that it is a Bernoulli flow. An important application are the STIT tessellation processes. |
| title | Regenerative processes for Poisson zero polytopes |
| topic | Probability 60D05, 60J25, 60J75, 37A25, 37A35 |
| url | https://arxiv.org/abs/1708.08592 |