On the points around which the planar Brownian motion winds frequently
We study the asymptotic behaviour of the area \(A_ n\) of the set of points around which the planar Brownian motion winds about \(n\) times on a given time-interval \([0,t]\). We prove that \(A_ n\) is equivalent (in the \(L^ 2\)-sense) to \(t/(2\pi n^ 2)\) as \(n\) tends to infinity.
asymptotic behaviour of the area \(A_ n\)
scientific article; zbMATH DE number 627489
scientific article