Conditioning to avoid zero via a class of concave functions for one-dimensional diffusions
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912610147893248 |
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| author | Yamato, Kosuke |
| author_facet | Yamato, Kosuke |
| contents | For one-dimensional diffusions on the half-line, we study a specific type of conditioning to avoid zero. We introduce supermartingales defined via concave functions with respect to the scale function. A conditioning is formulated through the exit times of the supermartingale, and its existence is shown. We also investigate the absolute continuity relations of the limit laws at time infinity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_14163 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Conditioning to avoid zero via a class of concave functions for one-dimensional diffusions Yamato, Kosuke Probability 60J60 For one-dimensional diffusions on the half-line, we study a specific type of conditioning to avoid zero. We introduce supermartingales defined via concave functions with respect to the scale function. A conditioning is formulated through the exit times of the supermartingale, and its existence is shown. We also investigate the absolute continuity relations of the limit laws at time infinity. |
| title | Conditioning to avoid zero via a class of concave functions for one-dimensional diffusions |
| topic | Probability 60J60 |
| url | https://arxiv.org/abs/2408.14163 |