Skellam Processes via Multiparameter Poisson Process
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914039678894080 |
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| author | Vishwakarma, Pradeep |
| author_facet | Vishwakarma, Pradeep |
| contents | We introduce a mltiparameter version of Skellam point process via multiparameter Poisson processes. Its distributional properties are studied in detail. Its compound representation is derived for a particular case. Also, its Riemann integral over a rectangle in $\mathbb{R}^M_+$, $M\ge1$ is introduced and a closed expression for its characteristic function is obtained. Later, we introduce a different version of multiparameter Skellam process, and derive a weak convergence result for it. Moreover, a two parameter fractional Skellam process is discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_12729 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Skellam Processes via Multiparameter Poisson Process Vishwakarma, Pradeep Probability 60G20, 60G55, 60G60 We introduce a mltiparameter version of Skellam point process via multiparameter Poisson processes. Its distributional properties are studied in detail. Its compound representation is derived for a particular case. Also, its Riemann integral over a rectangle in $\mathbb{R}^M_+$, $M\ge1$ is introduced and a closed expression for its characteristic function is obtained. Later, we introduce a different version of multiparameter Skellam process, and derive a weak convergence result for it. Moreover, a two parameter fractional Skellam process is discussed. |
| title | Skellam Processes via Multiparameter Poisson Process |
| topic | Probability 60G20, 60G55, 60G60 |
| url | https://arxiv.org/abs/2509.12729 |