PLANAR BROWNIAN MOTION WINDS EVENLY ALONG ITS TRAJECTORY

Isao Sauzedde (1)

1 LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation

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.

Domaines: Mathématiques [math]; Probabilités [math.PR]

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