Brownian motion with variable drift can be space-filling

الأصل · EN

For d ≥ 2 let B be standard d-dimensional Brownian motion. For any α< 1/d we construct an α-Hölder continuous function f [0,1] → Rᵈ 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).