Bernstein Fractional Derivatives: Censoring and Stochastic Processes
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909884683911168 |
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| author | Berger, David Li, Cailing Schilling, René L. |
| author_facet | Berger, David Li, Cailing Schilling, René L. |
| contents | We define censored fractional Bernstein derivatives on the positive half-line based on the Bernstein--Riemann--Liouville fractional derivative. The censored fractional derivative turns out to be the generator of the censored decreasing subordinator $S^c = (S_t^c)_{t\geq 0}$, which is obtained either via a pathwise construction by removing those jumps from the decreasing subordinator $(x-S_t)_{t\geq 0}$, $x>0$, that drive the path into negative territory, or via the Hille--Yosida theorem. Then we show that the censored decreasing subordinator has only finite life-time, and we identify various probability distributions related to $S^c$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_01760 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bernstein Fractional Derivatives: Censoring and Stochastic Processes Berger, David Li, Cailing Schilling, René L. Probability We define censored fractional Bernstein derivatives on the positive half-line based on the Bernstein--Riemann--Liouville fractional derivative. The censored fractional derivative turns out to be the generator of the censored decreasing subordinator $S^c = (S_t^c)_{t\geq 0}$, which is obtained either via a pathwise construction by removing those jumps from the decreasing subordinator $(x-S_t)_{t\geq 0}$, $x>0$, that drive the path into negative territory, or via the Hille--Yosida theorem. Then we show that the censored decreasing subordinator has only finite life-time, and we identify various probability distributions related to $S^c$. |
| title | Bernstein Fractional Derivatives: Censoring and Stochastic Processes |
| topic | Probability |
| url | https://arxiv.org/abs/2511.01760 |