Sharp barrier estimates for Bessel bridges
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912715121885184 |
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| author | Chiarini, Leandro Powell, Ellen |
| author_facet | Chiarini, Leandro Powell, Ellen |
| contents | In this article, we derive precise estimates for the probability that a Bessel bridge of dimension $d \ge 0$ and end points $x$ and $a+bT-j$ stays below the linear barrier $a + bt$ for all $t \in [0,T]$. We identify the leading order term as well as the asymptotic error for this probability as $T\to \infty$, depending on $a,b,j,x$. We also derive the behaviour of such leading term as we allow $a,j\to \infty$, and obtain precise bounds for all error terms. Finally, we establish a complementary result where the linear barrier is perturbed by a small concave function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_13416 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sharp barrier estimates for Bessel bridges Chiarini, Leandro Powell, Ellen Probability 60G40, 60J60, 60J65 In this article, we derive precise estimates for the probability that a Bessel bridge of dimension $d \ge 0$ and end points $x$ and $a+bT-j$ stays below the linear barrier $a + bt$ for all $t \in [0,T]$. We identify the leading order term as well as the asymptotic error for this probability as $T\to \infty$, depending on $a,b,j,x$. We also derive the behaviour of such leading term as we allow $a,j\to \infty$, and obtain precise bounds for all error terms. Finally, we establish a complementary result where the linear barrier is perturbed by a small concave function. |
| title | Sharp barrier estimates for Bessel bridges |
| topic | Probability 60G40, 60J60, 60J65 |
| url | https://arxiv.org/abs/2511.13416 |