On Multiparameter Generalized Counting Process and its Time-Changed Variants
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908574024728576 |
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| author | Dhillon, Manisha Kataria, Kuldeep Kumar |
| author_facet | Dhillon, Manisha Kataria, Kuldeep Kumar |
| contents | We introduce and study a multiparameter version of the generalized counting process (GCP), where there is a possibility of finitely many arrivals simultaneously. We call it the multiparameter GCP. In a particular case, it is uniquely represented as a weighted sum of independent multiparameter Poisson processes. For a specific case, we establish a relationship between the multiparameter GCP and the sum of independent GCPs. Some of its time-changed variants are studied where the time-changing components used are the multiparameter stable subordinator and the multiparameter inverse stable subordinator. An integral of the multiparameter GCP is defined, and its asymptotic distribution is obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_23070 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Multiparameter Generalized Counting Process and its Time-Changed Variants Dhillon, Manisha Kataria, Kuldeep Kumar Probability Primary: 60G51, 60G44, Secondary: 60G60 We introduce and study a multiparameter version of the generalized counting process (GCP), where there is a possibility of finitely many arrivals simultaneously. We call it the multiparameter GCP. In a particular case, it is uniquely represented as a weighted sum of independent multiparameter Poisson processes. For a specific case, we establish a relationship between the multiparameter GCP and the sum of independent GCPs. Some of its time-changed variants are studied where the time-changing components used are the multiparameter stable subordinator and the multiparameter inverse stable subordinator. An integral of the multiparameter GCP is defined, and its asymptotic distribution is obtained. |
| title | On Multiparameter Generalized Counting Process and its Time-Changed Variants |
| topic | Probability Primary: 60G51, 60G44, Secondary: 60G60 |
| url | https://arxiv.org/abs/2503.23070 |