Some Compound Fractional Poisson Processes
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866909248684818432 |
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| author | Khandakar, M. Kataria, K. K. |
| author_facet | Khandakar, M. Kataria, K. K. |
| contents | In this paper, we introduce and study fractional versions of three compound Poisson processes, namely, the Bell-Touchard process, the Poisson-logarithmic process and the generalized Pólya-Aeppli process. It is shown that these processes are limiting cases of a recently introduced process by Di Crescenzo et al. (2016), namely, the generalized counting process. We obtain the mean, variance, covariance, long-range dependence property etc. for these processes. Also, we obtain several equivalent forms of the one-dimensional distribution of fractional versions of these processes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_04377 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Some Compound Fractional Poisson Processes Khandakar, M. Kataria, K. K. Probability 60G22, 60G51 In this paper, we introduce and study fractional versions of three compound Poisson processes, namely, the Bell-Touchard process, the Poisson-logarithmic process and the generalized Pólya-Aeppli process. It is shown that these processes are limiting cases of a recently introduced process by Di Crescenzo et al. (2016), namely, the generalized counting process. We obtain the mean, variance, covariance, long-range dependence property etc. for these processes. Also, we obtain several equivalent forms of the one-dimensional distribution of fractional versions of these processes. |
| title | Some Compound Fractional Poisson Processes |
| topic | Probability 60G22, 60G51 |
| url | https://arxiv.org/abs/2206.04377 |