Electronic Communications in Probability

Where does a random process hit a fractal barrier?

Itai Benjamini and Alexander Shamov

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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.

Article information

Electron. Commun. Probab., Volume 23 (2018), paper no. 25, 5 pp.

Received: 4 August 2016
Accepted: 5 April 2018
First available in Project Euclid: 28 April 2018

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Primary: subversive math

fractal harmonic measure

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Benjamini, Itai; Shamov, Alexander. Where does a random process hit a fractal barrier?. Electron. Commun. Probab. 23 (2018), paper no. 25, 5 pp. doi:10.1214/18-ECP131. https://projecteuclid.org/euclid.ecp/1524881133

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