Analytic property of generalized scale functions for standard processes with no negative jumps and its application to quasi-stationary distributions
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866914855278084096 |
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| author | Noba, Kei Yamato, Kosuke |
| author_facet | Noba, Kei Yamato, Kosuke |
| contents | For a generalized scale function of standard processes, we characterize it as a unique solution to a Volterra type integral equation. This allows us to extend it to an entire function and to derive a useful identity that we call the resolvent identity. We apply this result to study the existence of a quasi-stationary distribution for the processes killed at hitting boundaries. A new classification of the boundary, which is a natural extension of Feller's for one-dimensional diffusions, is introduced and plays a central role to characterize the existence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_09935 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Analytic property of generalized scale functions for standard processes with no negative jumps and its application to quasi-stationary distributions Noba, Kei Yamato, Kosuke Probability 60J76 For a generalized scale function of standard processes, we characterize it as a unique solution to a Volterra type integral equation. This allows us to extend it to an entire function and to derive a useful identity that we call the resolvent identity. We apply this result to study the existence of a quasi-stationary distribution for the processes killed at hitting boundaries. A new classification of the boundary, which is a natural extension of Feller's for one-dimensional diffusions, is introduced and plays a central role to characterize the existence. |
| title | Analytic property of generalized scale functions for standard processes with no negative jumps and its application to quasi-stationary distributions |
| topic | Probability 60J76 |
| url | https://arxiv.org/abs/2308.09935 |