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arXiv · 2404.09333

Small deviation for the mutual intersection local time of Brownian motions

Xia Chen·Jian Song
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Abstract

In this note, we establish the bounds \[ c\varepsilon^{\frac23}\le P\bigg\{\int_0^1\!\!\int_0^1\delta_0(B_s-\tilde{B}_r)dsdr\le \varepsilon \bigg\} \le C \varepsilon^{\frac23},\] for the mutual intersection local time of two independent 1-dimensional Brownian motions $B$ and $\tilde B$.

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Xia Chen, Jian Song. 2024-04-14. Small deviation for the mutual intersection local time of Brownian motions. https://arxiv.org/abs/2404.09333

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