LÉVY AREA WITHOUT APPROXIMATION

Isao Sauzedde (1)

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

We give asymptotic estimations on the area of the sets of points with large Brownian winding, and study the average winding between a planar Brownian motion and a Poisson point process of large intensity on the plane. This allows us to give a new denition of the Lévy area which does not rely on approximations of the Brownian path. It also does not depend on the metric structure on the plane.

Mots clés: Stokes' formula; Planar Brownian motion; Lévy's area

Domaines: Probabilités [math.PR]

Isao Sauzedde. LÉVY AREA WITHOUT APPROXIMATION. 2021. ⟨hal-03107197⟩