English

Where does a random process hit a fractal barrier?

Probability 2016-08-05 v2

Abstract

Given a Brownian path β(t)\beta(t) on R\mathbb{R}, starting at 11, a.s. there is a singular time set TβT_{\beta}, such that the first hitting time of β\beta by an independent Brownian motion, starting at 00, is in TβT_{\beta} with probability one. A couple of problems regarding hitting measure for random processes are presented.

Cite

@article{arxiv.1608.00505,
  title  = {Where does a random process hit a fractal barrier?},
  author = {Itai Benjamini and Alexander Shamov},
  journal= {arXiv preprint arXiv:1608.00505},
  year   = {2016}
}
R2 v1 2026-06-22T15:09:17.477Z