A probabilistic representation of the derivative of a one dimensional killed diffusion semigroup
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866910475936071680 |
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| author | Crisan, Dan Kohatsu-Higa, Arturo |
| author_facet | Crisan, Dan Kohatsu-Higa, Arturo |
| contents | We provide a probabilistic representation for the derivative of the semigroup corresponding to a diffusion process killed at the boundary of a half interval. In particular, we show that the derivative of the semi-group can be expressed as the expected value of a functional of a reflected diffusion process. Furthermore, as an application, we obtain a Bismut-Elworthy-Li formula which is also valid at the boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_07084 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A probabilistic representation of the derivative of a one dimensional killed diffusion semigroup Crisan, Dan Kohatsu-Higa, Arturo Probability 60H10, 60J60, 60G40 We provide a probabilistic representation for the derivative of the semigroup corresponding to a diffusion process killed at the boundary of a half interval. In particular, we show that the derivative of the semi-group can be expressed as the expected value of a functional of a reflected diffusion process. Furthermore, as an application, we obtain a Bismut-Elworthy-Li formula which is also valid at the boundary. |
| title | A probabilistic representation of the derivative of a one dimensional killed diffusion semigroup |
| topic | Probability 60H10, 60J60, 60G40 |
| url | https://arxiv.org/abs/2312.07084 |