## Electronic Communications in Probability

### Where does a random process hit a fractal barrier?

#### 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.

#### Article information

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

Dates
Accepted: 5 April 2018
First available in Project Euclid: 28 April 2018

https://projecteuclid.org/euclid.ecp/1524881133

Digital Object Identifier
doi:10.1214/18-ECP131

Mathematical Reviews number (MathSciNet)
MR3798236

Zentralblatt MATH identifier
1398.60087

Subjects
Primary: subversive math

Keywords
fractal harmonic measure

#### Citation

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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