A limit theorem for certain Feller semigroups, and the distribution of the local time for Brownian motion when it exits an interval
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918142203133952 |
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| author | Bobrowski, Adam Pilipenko, Andrey |
| author_facet | Bobrowski, Adam Pilipenko, Andrey |
| contents | We consider local singular perturbations of a one-dimensional Laplace operator from the point of view of semigroup theory. Under certain assumptions, we prove the convergence of the corresponding semigroups to the heat semigroup with Robin-type boundary conditions at zero. As an application we provide semigroup theoretical approach to calculating the distribution of the local time for Brownian motion when it exits an interval. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_13076 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A limit theorem for certain Feller semigroups, and the distribution of the local time for Brownian motion when it exits an interval Bobrowski, Adam Pilipenko, Andrey Probability 60J35, 47D07 We consider local singular perturbations of a one-dimensional Laplace operator from the point of view of semigroup theory. Under certain assumptions, we prove the convergence of the corresponding semigroups to the heat semigroup with Robin-type boundary conditions at zero. As an application we provide semigroup theoretical approach to calculating the distribution of the local time for Brownian motion when it exits an interval. |
| title | A limit theorem for certain Feller semigroups, and the distribution of the local time for Brownian motion when it exits an interval |
| topic | Probability 60J35, 47D07 |
| url | https://arxiv.org/abs/2509.13076 |