Small deviation for the mutual intersection local time of Brownian motions

Xia Chen; Jian Song

Small deviation for the mutual intersection local time of Brownian motions

Probability 2024-04-16 v1

Authors: Xia Chen , Jian Song

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 $\tilde B$ .

Keywords

small deviation mutual intersection local time Brownian motion probability bounds

Cite

@article{arxiv.2404.09333,
  title  = {Small deviation for the mutual intersection local time of Brownian motions},
  author = {Xia Chen and Jian Song},
  journal= {arXiv preprint arXiv:2404.09333},
  year   = {2024}
}

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