Open Access
Translator Disclaimer
January, 1988 Self-Intersection Gauge for Random Walks and for Brownian Motion
E. B. Dynkin
Ann. Probab. 16(1): 1-57 (January, 1988). DOI: 10.1214/aop/1176991884


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.


Download Citation

E. B. Dynkin. "Self-Intersection Gauge for Random Walks and for Brownian Motion." Ann. Probab. 16 (1) 1 - 57, January, 1988.


Published: January, 1988
First available in Project Euclid: 19 April 2007

zbMATH: 0638.60081
MathSciNet: MR920254
Digital Object Identifier: 10.1214/aop/1176991884

Primary: 60G60
Secondary: 60J55 , 60J65

Keywords: multiple points of random walks and of the Brownian motion , self-intersection gauges , Self-intersection local times , the invariance principle

Rights: Copyright © 1988 Institute of Mathematical Statistics


Vol.16 • No. 1 • January, 1988
Back to Top