Brownian bricklayer: a random space-filling curve

2017/08/23 by Forman, Noah
#60G17 #60J55 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1708.07172

Abstract

Let (B(t), t≥0) denote the standard, one-dimensional Wiener process and (ℓ(y,t); y∈ℝ, t≥0) its local time at level y up to time t. Then ( (B(t), ℓ(B(t),t)), t≥0 ) is a random path that fills the upper half-plane, covering one unit of area per unit time.

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