Lévy processes with jumps governed by lower incomplete gamma subordinator and its variations
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866914797320142848 |
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| author | Babulal, Meena Sanjay Gauttam, Sunil Kumar Maheshwari, Aditya |
| author_facet | Babulal, Meena Sanjay Gauttam, Sunil Kumar Maheshwari, Aditya |
| contents | In this paper, we study the Lévy process time-changed by independent Lévy subordinators, namely, the incomplete gamma subordinator, the $ε$-jumps incomplete gamma subordinator and tempered incomplete gamma subordinator. We derive their important distributional properties such as mean, variance, correlation, tail probabilities and fractional moments. The long-range dependence property of these processes are discussed. An application in insurance domain is studied in detail. Finally, we present the simulated sample paths for the subordinators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_17330 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Lévy processes with jumps governed by lower incomplete gamma subordinator and its variations Babulal, Meena Sanjay Gauttam, Sunil Kumar Maheshwari, Aditya Probability 60G51, 60G55 In this paper, we study the Lévy process time-changed by independent Lévy subordinators, namely, the incomplete gamma subordinator, the $ε$-jumps incomplete gamma subordinator and tempered incomplete gamma subordinator. We derive their important distributional properties such as mean, variance, correlation, tail probabilities and fractional moments. The long-range dependence property of these processes are discussed. An application in insurance domain is studied in detail. Finally, we present the simulated sample paths for the subordinators. |
| title | Lévy processes with jumps governed by lower incomplete gamma subordinator and its variations |
| topic | Probability 60G51, 60G55 |
| url | https://arxiv.org/abs/2303.17330 |