Brownian motion with variable drift can be space-filling

Details Brownian motion with variable drift can be space-filling Brownian motion with variable drift can be space-filling

2010-03-01

arxiv.org/abs/1003.0228v1

Mathematics

Probability

15 pages, 3 figures

Scientific paper

For $d \geq 2$ let $B$ be standard $d$-dimensional Brownian motion. For any
$\alpha < 1/d$ we construct an $\alpha$-H\"{o}lder continuous function $f
\colon [0,1] \to \mathbb{R}^d$ so that the range of $B-f$ covers an open set.
This strengthens a result of Graversen (1982) and answers a question of Le Gall
(1988).

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