Dynkin, E. B. Regularized self-intersection local times of planar Brownian motion. (English) Zbl 0641.60085 Ann. Probab. 16, No. 1, 58-74 (1988). 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 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. Reviewer: J.Le Gall Cited in 19 Documents MSC: 60J65 Brownian motion 60J55 Local time and additive functionals 60G60 Random fields Keywords:self-intersections of a planar Brownian motion; local times PDFBibTeX XMLCite \textit{E. B. Dynkin}, Ann. Probab. 16, No. 1, 58--74 (1988; Zbl 0641.60085) Full Text: DOI