A Functional Central Limit Theorem for the General Brownian Motion on the Half-Line
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913577069182976 |
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| author | Erhard, Dirk Franco, Tertuliano Jara, Milton Pimenta, Eduardo |
| author_facet | Erhard, Dirk Franco, Tertuliano Jara, Milton Pimenta, Eduardo |
| contents | In this work, we establish a Trotter-Kato type theorem. More precisely, we characterize the convergence in distribution of Feller processes by examining the convergence of their generators. The main novelty lies in providing quantitative estimates in the vague topology at any fixed time. As important applications, we deduce functional central limit theorems for random walks on the positive integers with boundary conditions, which converge to Brownian motions on the positive half-line with boundary conditions at zero. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_06830 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Functional Central Limit Theorem for the General Brownian Motion on the Half-Line Erhard, Dirk Franco, Tertuliano Jara, Milton Pimenta, Eduardo Probability 60F17, 60F05, 60J65, 60J27 In this work, we establish a Trotter-Kato type theorem. More precisely, we characterize the convergence in distribution of Feller processes by examining the convergence of their generators. The main novelty lies in providing quantitative estimates in the vague topology at any fixed time. As important applications, we deduce functional central limit theorems for random walks on the positive integers with boundary conditions, which converge to Brownian motions on the positive half-line with boundary conditions at zero. |
| title | A Functional Central Limit Theorem for the General Brownian Motion on the Half-Line |
| topic | Probability 60F17, 60F05, 60J65, 60J27 |
| url | https://arxiv.org/abs/2408.06830 |