Tempered space-time fractional negative binomial process
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917773023641600 |
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| author | Shilpa Pathak, Ashok Kumar Maheshwari, Aditya |
| author_facet | Shilpa Pathak, Ashok Kumar Maheshwari, Aditya |
| contents | In this paper, we define a tempered space-time fractional negative binomial process (TSTFNBP) by subordinating the fractional Poisson process with an independent tempered Mittag-Leffler Lévy subordinator. We study its distributional properties and its connection to partial differential equations. We derive the asymptotic behavior of its fractional order moments and long-range dependence property. It is shown that the TSTFNBP exhibits overdispersion. We also obtain some results related to the first-passage time. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_07044 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tempered space-time fractional negative binomial process Shilpa Pathak, Ashok Kumar Maheshwari, Aditya Probability 60G22, 60G51 In this paper, we define a tempered space-time fractional negative binomial process (TSTFNBP) by subordinating the fractional Poisson process with an independent tempered Mittag-Leffler Lévy subordinator. We study its distributional properties and its connection to partial differential equations. We derive the asymptotic behavior of its fractional order moments and long-range dependence property. It is shown that the TSTFNBP exhibits overdispersion. We also obtain some results related to the first-passage time. |
| title | Tempered space-time fractional negative binomial process |
| topic | Probability 60G22, 60G51 |
| url | https://arxiv.org/abs/2409.07044 |