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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.09333 |
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| _version_ | 1866913314842345472 |
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| author | Chen, Xia Song, Jian |
| author_facet | Chen, Xia Song, Jian |
| contents | In this note, we establish the bounds \[ c\varepsilon^{\frac23}\le P\bigg\{\int_0^1\!\!\int_0^1δ_0(B_s-\tilde{B}_r)dsdr\le \varepsilon \bigg\} \le C \varepsilon^{\frac23},\] for the mutual intersection local time of two independent 1-dimensional Brownian motions $B$ and $\tilde B$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_09333 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Small deviation for the mutual intersection local time of Brownian motions Chen, Xia Song, Jian Probability In this note, we establish the bounds \[ c\varepsilon^{\frac23}\le P\bigg\{\int_0^1\!\!\int_0^1δ_0(B_s-\tilde{B}_r)dsdr\le \varepsilon \bigg\} \le C \varepsilon^{\frac23},\] for the mutual intersection local time of two independent 1-dimensional Brownian motions $B$ and $\tilde B$. |
| title | Small deviation for the mutual intersection local time of Brownian motions |
| topic | Probability |
| url | https://arxiv.org/abs/2404.09333 |