Regularized self-intersection local times of planar Brownian motion (Q1100811)

This paper is devoted to the construction of functionals associated with the k-multiple self-intersections of a planar Brownian motion. Such functionals are often called renormalized self-intersection local times, and were introduced in the case of double points \((k=2)\) by \textit{S. R. S. Varadhan} [Appendix to K. Symanzik, Euclidean quantum field theory. In R. Jost (ed.), Local quantum theory (1969)]. The general case is significantly more difficult: The author gives various constructions which lead to the same functionals. The moments of these functionals are explicitly computed.