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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.26156 |
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| _version_ | 1866915586751070208 |
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| author | Khandakar, Mostafizar Pal, Bratati Vellaisamy, Palaniappan |
| author_facet | Khandakar, Mostafizar Pal, Bratati Vellaisamy, Palaniappan |
| contents | In this paper, we introduce and study two time-changed variants of the generalized fractional Skellam process. These are obtained by time-changing the generalized fractional Skellam process with an independent Lévy subordinator with finite moments of any order and its inverse, respectively. We call the introduced processes the time-changed generalized fractional Skellam process-I (TCGFSP-I) and the time-changed generalized fractional Skellam process-II (TCGFSP-II), respectively. The probability generating function, moment generating function, moments, factorial moments, variance, covariance, {\it etc.}, are derived for the TCGFSP-I. We obtain a variant of the law of the iterated logarithm for it and establish its long-range dependence property. Several special cases of the TCGFSP-I are considered, and the associated system of governing differential equations is obtained. Later, some distributional properties and particular cases are discussed for the TCGFSP-II. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_26156 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Time-changed generalized fractional Skellam process Khandakar, Mostafizar Pal, Bratati Vellaisamy, Palaniappan Probability In this paper, we introduce and study two time-changed variants of the generalized fractional Skellam process. These are obtained by time-changing the generalized fractional Skellam process with an independent Lévy subordinator with finite moments of any order and its inverse, respectively. We call the introduced processes the time-changed generalized fractional Skellam process-I (TCGFSP-I) and the time-changed generalized fractional Skellam process-II (TCGFSP-II), respectively. The probability generating function, moment generating function, moments, factorial moments, variance, covariance, {\it etc.}, are derived for the TCGFSP-I. We obtain a variant of the law of the iterated logarithm for it and establish its long-range dependence property. Several special cases of the TCGFSP-I are considered, and the associated system of governing differential equations is obtained. Later, some distributional properties and particular cases are discussed for the TCGFSP-II. |
| title | Time-changed generalized fractional Skellam process |
| topic | Probability |
| url | https://arxiv.org/abs/2510.26156 |