The Annals of Probability
- Ann. Probab.
- Volume 16, Number 1 (1988), 1-57.
Self-Intersection Gauge for Random Walks and for Brownian Motion
A class of random fields associated with multiple points of a random walk in the plane is studied. It is proved that these fields converge in distribution to analogous fields measuring self-intersections of the planar Brownian motion. The concluding section contains a survey of literature on intersection local times and their renormalizations. A brief look through the first pages of this section could provide the reader with additional motivation for the present work.
Ann. Probab., Volume 16, Number 1 (1988), 1-57.
First available in Project Euclid: 19 April 2007
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Dynkin, E. B. Self-Intersection Gauge for Random Walks and for Brownian Motion. Ann. Probab. 16 (1988), no. 1, 1--57. doi:10.1214/aop/1176991884. https://projecteuclid.org/euclid.aop/1176991884