Generalized Space-Fractional Poisson Process via Variable-Order Stable Subordinator
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908757158526976 |
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| author | Singh, Reetendra Maheshwari, Aditya |
| author_facet | Singh, Reetendra Maheshwari, Aditya |
| contents | This paper introduces a variable-order stable subordinator (VOSS) $S^{α(t)}(t)$ with index $α(t)\in(0,1)$, where $α(t)$ is a right-continuous piecewise constant function. We drive the Generalized Space-Fractional Poisson Process via Variable-Order Stable Subordinator (GSFPP-VO) defined by $\{N(S^{α(t)}(t))\}_{t \geq 0}$, obtained by time-changing a homogeneous Poisson process $\{N(t,λ)\}_{t\geq 0}$ with rate parameter $λ>0$ by an independent VOSS. Explicit expressions for the Laplace transform, probability generating function, probability mass function, and moment generating function of the GSFPP-VO are derived, and these quantities are shown to satisfy partial differential equations. Finally, we establish the associated generalized distributions, analyze the hitting-time properties, and characterize the Lévy measures of the GSFPP-VO. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_06808 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Generalized Space-Fractional Poisson Process via Variable-Order Stable Subordinator Singh, Reetendra Maheshwari, Aditya Probability 60G55, 60G22 This paper introduces a variable-order stable subordinator (VOSS) $S^{α(t)}(t)$ with index $α(t)\in(0,1)$, where $α(t)$ is a right-continuous piecewise constant function. We drive the Generalized Space-Fractional Poisson Process via Variable-Order Stable Subordinator (GSFPP-VO) defined by $\{N(S^{α(t)}(t))\}_{t \geq 0}$, obtained by time-changing a homogeneous Poisson process $\{N(t,λ)\}_{t\geq 0}$ with rate parameter $λ>0$ by an independent VOSS. Explicit expressions for the Laplace transform, probability generating function, probability mass function, and moment generating function of the GSFPP-VO are derived, and these quantities are shown to satisfy partial differential equations. Finally, we establish the associated generalized distributions, analyze the hitting-time properties, and characterize the Lévy measures of the GSFPP-VO. |
| title | Generalized Space-Fractional Poisson Process via Variable-Order Stable Subordinator |
| topic | Probability 60G55, 60G22 |
| url | https://arxiv.org/abs/2601.06808 |