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Brownian motion with variable drift can be space-filling

2010/03/01 by Antunović, Tonći, Peres, Yuval, Vermesi, Brigitta
#26A16 #26A30 #28A80 #60J65 #FOS: Mathematics #Metric Geometry (math.MG) #Probability (math.PR)

paper · doi:10.48550/arxiv.1003.0228

Abstract

For d ≥ 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] → 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).

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