Method of Filtration in first passage time problems
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913476314660864 |
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| author | Sakamoto, Yuta Sakaue, Takahiro |
| author_facet | Sakamoto, Yuta Sakaue, Takahiro |
| contents | Statistics of stochastic processes are crucially influenced by the boundary conditions. In one spatial dimension, for example, the first passage time distribution in semi-infinite space (one absorbing boundary) is markedly different from that in a finite interval with two absorbing boundaries. Here, we propose a method, which we refer to as a method of filtration, that allows us to construct the latter from only the knowledge of the former. We demonstrate that our method yields two solution forms, a method of eigenfunction expansion-like form and a method of image-like form. In particular, we argue that the latter solution form is a generalization of the method of image applicable to a stochastic process for which the method of image generally does not work, e.g., the Ornstein-Uhlenbeck process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_11815 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Method of Filtration in first passage time problems Sakamoto, Yuta Sakaue, Takahiro Mathematical Physics Statistics of stochastic processes are crucially influenced by the boundary conditions. In one spatial dimension, for example, the first passage time distribution in semi-infinite space (one absorbing boundary) is markedly different from that in a finite interval with two absorbing boundaries. Here, we propose a method, which we refer to as a method of filtration, that allows us to construct the latter from only the knowledge of the former. We demonstrate that our method yields two solution forms, a method of eigenfunction expansion-like form and a method of image-like form. In particular, we argue that the latter solution form is a generalization of the method of image applicable to a stochastic process for which the method of image generally does not work, e.g., the Ornstein-Uhlenbeck process. |
| title | Method of Filtration in first passage time problems |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2405.11815 |