Lévy area without approximation (Q2083872)

Stokes' theorem is pointless in the case of Brownian motion. In this paper asymptotic estimations on the area of the set of points with large Brownian winding are studied and the average winding between a planar Brownian motion and a Poisson point process of large intensity on the plane are considered. The author uses a different family of approximations and proves an almost sure convergence. By this action a new definition of the Lévy area which does not rely on piecewise linear approximations of the Brownian path is given. The result of the paper is worth noticing and the paper is worth reading.