The Annals of Probability

Self-Intersection Gauge for Random Walks and for Brownian Motion

E. B. Dynkin

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Abstract

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.

Article information

Source
Ann. Probab., Volume 16, Number 1 (1988), 1-57.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176991884

Digital Object Identifier
doi:10.1214/aop/1176991884

Mathematical Reviews number (MathSciNet)
MR920254

Zentralblatt MATH identifier
0638.60081

JSTOR
links.jstor.org

Subjects
Primary: 60G60: Random fields
Secondary: 60J55: Local time and additive functionals 60J65: Brownian motion [See also 58J65]

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

Citation

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


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