Where does a random process hit a fractal barrier?

Itai Benjamini; Alexander Shamov

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arXiv · 1608.00505

Where does a random process hit a fractal barrier?

Itai Benjamini·Alexander Shamov

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Abstract

Given a Brownian path $\beta(t)$ on $\mathbb{R}$, starting at $1$, a.s. there is a singular time set $T_{\beta}$, such that the first hitting time of $\beta$ by an independent Brownian motion, starting at $0$, is in $T_{\beta}$ with probability one. A couple of problems regarding hitting measure for random processes are presented.

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Itai Benjamini, Alexander Shamov. 2016-08-01. Where does a random process hit a fractal barrier?. https://arxiv.org/abs/1608.00505

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