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arXiv · 1003.0228

Brownian motion with variable drift can be space-filling

Tonći Antunović·Yuval Peres·Brigitta Vermesi
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Abstract

For $d \geq 2$ let $B$ be standard $d$-dimensional Brownian motion. For any $α< 1/d$ we construct an $α$-Hölder 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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Tonći Antunović, Yuval Peres, Brigitta Vermesi. 2010-03-01. Brownian motion with variable drift can be space-filling. https://arxiv.org/abs/1003.0228

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