On the singularities of the intersection local times of planar Brownian motion
The singularities of intersection local times for multiple points of two- dimensional Brownian motion are considered. Using Dynkin's approach to renormalization, the author obtains an asymptotic expansion for the behavior of the \(p\)-multiple self-intersection local time of a planar Brownian motion at a point \(y \in (\mathbb{R}^ 2)^{p-1}\), when one or several coordinates of \(y\) go to 0. Also another renormalization of intersection local times, by using methods of stochastic calculus, is considered.
singularities of intersection local times
renormalization of intersection local times
scientific article; zbMATH DE number 566219