Brownian bricklayer: A random space-filling curve

Noah Forman

Statistics & Probability Letters, 2018, vol. 143, issue C, 43-46

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, continuous path that fills the upper half-plane, covering one unit of area per unit time.

Keywords: Local times; Space-filling curve; Brownian motion (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1016/j.spl.2018.07.010

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