The Annals of Probability

Random Walks and Intersection Local Time

Jay Rosen

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Abstract

With each random walk on $\mathbb{Z}^2$ we associate a functional related to the number of steps which the walk spends in sites occupied at least $k$ times. We show that if our random walk is in the domain of attraction of a stable process of order greater than $2(2k - 2)/(2k - 1)$, then our functional coverges to the intersection local time of the limiting process.

Article information

Source
Ann. Probab., Volume 18, Number 3 (1990), 959-977.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176990731

Digital Object Identifier
doi:10.1214/aop/1176990731

Mathematical Reviews number (MathSciNet)
MR1062054

Zentralblatt MATH identifier
0717.60057

JSTOR
links.jstor.org

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

Keywords
Random walks intersection local time multiple points domain of attraction

Citation

Rosen, Jay. Random Walks and Intersection Local Time. Ann. Probab. 18 (1990), no. 3, 959--977. doi:10.1214/aop/1176990731. https://projecteuclid.org/euclid.aop/1176990731


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