Multiparameter Poisson Processes and Martingales
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929678460125184 |
|---|---|
| author | Vishwakarma, P. Kataria, K. K. |
| author_facet | Vishwakarma, P. Kataria, K. K. |
| contents | We introduce and study a multiparameter Poisson process (MPP). In a particular case, it is observed that the MPP has a unique representation. Its subordination with the multivariate subordinator and inverse subordinator are studied in detail. Also, we consider a multivariate multiparameter Poisson process and establish its connection with the MPP. An integral of the MPP is defined, and its asymptotic distribution is obtained. Later, we study some properties of the multiparameter martingales. Moreover, the multiparameter martingale characterizations for the MPP and its subordinated variants are derived. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_09543 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multiparameter Poisson Processes and Martingales Vishwakarma, P. Kataria, K. K. Probability Primary: 60G51, 60G60, Secondary: 60G44 We introduce and study a multiparameter Poisson process (MPP). In a particular case, it is observed that the MPP has a unique representation. Its subordination with the multivariate subordinator and inverse subordinator are studied in detail. Also, we consider a multivariate multiparameter Poisson process and establish its connection with the MPP. An integral of the MPP is defined, and its asymptotic distribution is obtained. Later, we study some properties of the multiparameter martingales. Moreover, the multiparameter martingale characterizations for the MPP and its subordinated variants are derived. |
| title | Multiparameter Poisson Processes and Martingales |
| topic | Probability Primary: 60G51, 60G60, Secondary: 60G44 |
| url | https://arxiv.org/abs/2501.09543 |