Short proof of the conditioning property for multi-dimensional Poisson point processes
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914013271556096 |
|---|---|
| author | Lanchier, Nicolas |
| author_facet | Lanchier, Nicolas |
| contents | Poisson processes and one-dimensional Poisson point processes satisfy three main properties: superposition, thinning, and conditioning. The proof of the first two relies on basic estimates involving the Poisson distribution that are also true for multi-dimensional Poisson point processes. In contrast, the proof of conditioning uses that the distances between consecutive occurrences in time or entities in space are independent and exponentially distributed, which is nonsensical in higher dimensions. This paper gives a short proof of the conditioning property for multi-dimensional Poisson point processes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_21303 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Short proof of the conditioning property for multi-dimensional Poisson point processes Lanchier, Nicolas Probability 60G55 Poisson processes and one-dimensional Poisson point processes satisfy three main properties: superposition, thinning, and conditioning. The proof of the first two relies on basic estimates involving the Poisson distribution that are also true for multi-dimensional Poisson point processes. In contrast, the proof of conditioning uses that the distances between consecutive occurrences in time or entities in space are independent and exponentially distributed, which is nonsensical in higher dimensions. This paper gives a short proof of the conditioning property for multi-dimensional Poisson point processes. |
| title | Short proof of the conditioning property for multi-dimensional Poisson point processes |
| topic | Probability 60G55 |
| url | https://arxiv.org/abs/2508.21303 |