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Regularized self-intersection local times of planar Brownian motion. (English) Zbl 0641.60085

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

MSC:

60J65 Brownian motion
60J55 Local time and additive functionals
60G60 Random fields
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