PLANAR BROWNIAN MOTION WINDS EVENLY ALONG ITS TRAJECTORY - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2021

PLANAR BROWNIAN MOTION WINDS EVENLY ALONG ITS TRAJECTORY

Résumé

Let D_N be the set of points around which a planar Brownian motion winds at least N times. We prove that the random measure on the plane with density 2πN D_N with respect to the Lebesgue measure converges almost surely weakly, as N tends to infinity, towards the occupation measure of the Brownian motion.
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Dates et versions

hal-03186807 , version 1 (31-03-2021)

Identifiants

  • HAL Id : hal-03186807 , version 1

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Isao Sauzedde. PLANAR BROWNIAN MOTION WINDS EVENLY ALONG ITS TRAJECTORY. 2021. ⟨hal-03186807⟩
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