On the Palm distribution of superposition of point processes
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908508953247744 |
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| author | Beraha, Mario Camerlenghi, Federico |
| author_facet | Beraha, Mario Camerlenghi, Federico |
| contents | Palm distributions are critical in the study of point processes. In the present paper we focus on a point process $Φ$ defined as the superposition, i.e., sum, of two independent point processes, say $Φ= Φ_1 + Φ_2$, and we characterize its Palm distribution. In particular, we show that the Palm distribution of $Φ$ admits a simple mixture representation depending only on the Palm distribution of $Φ_j$, as $j=1, 2$, and the associated moment measures. Extensions to the superposition of multiple point processes, and higher order Palm distributions, are treated analogously. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_14753 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Palm distribution of superposition of point processes Beraha, Mario Camerlenghi, Federico Probability Statistics Theory Palm distributions are critical in the study of point processes. In the present paper we focus on a point process $Φ$ defined as the superposition, i.e., sum, of two independent point processes, say $Φ= Φ_1 + Φ_2$, and we characterize its Palm distribution. In particular, we show that the Palm distribution of $Φ$ admits a simple mixture representation depending only on the Palm distribution of $Φ_j$, as $j=1, 2$, and the associated moment measures. Extensions to the superposition of multiple point processes, and higher order Palm distributions, are treated analogously. |
| title | On the Palm distribution of superposition of point processes |
| topic | Probability Statistics Theory |
| url | https://arxiv.org/abs/2409.14753 |