Geometrical subordinated Poisson processes and its extensions
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917936712646656 |
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| author | Gupta, Neha Maheshwari, Aditya Goyal, Dheeraj |
| author_facet | Gupta, Neha Maheshwari, Aditya Goyal, Dheeraj |
| contents | In this paper, we study a generalized version of the Poisson-type process by time-changing it with the geometric counting process. Our work generalizes the work done by Meoli (2023) \cite{meoli2023some}. We defined the geometric subordinated Poisson process (GSPP), the geometric subordinated compound Poisson process (GSCPP) and the geometric subordinated multiplicative Poisson process (GSMPP) by time-changing the subordinated Poisson process, subordinated compound Poisson process and subordinated multiplicative Poisson process with the geometric counting process, respectively. We derived several distributional properties and many special cases from the above-mentioned processes. We calculate the asymptotic behavior of the correlation structure. We have discussed applications of time-changed generalized compound Poisson in shock modelling. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_18951 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometrical subordinated Poisson processes and its extensions Gupta, Neha Maheshwari, Aditya Goyal, Dheeraj Probability 60G55, 60G22 In this paper, we study a generalized version of the Poisson-type process by time-changing it with the geometric counting process. Our work generalizes the work done by Meoli (2023) \cite{meoli2023some}. We defined the geometric subordinated Poisson process (GSPP), the geometric subordinated compound Poisson process (GSCPP) and the geometric subordinated multiplicative Poisson process (GSMPP) by time-changing the subordinated Poisson process, subordinated compound Poisson process and subordinated multiplicative Poisson process with the geometric counting process, respectively. We derived several distributional properties and many special cases from the above-mentioned processes. We calculate the asymptotic behavior of the correlation structure. We have discussed applications of time-changed generalized compound Poisson in shock modelling. |
| title | Geometrical subordinated Poisson processes and its extensions |
| topic | Probability 60G55, 60G22 |
| url | https://arxiv.org/abs/2502.18951 |