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.
Citation
Jay Rosen. "Random Walks and Intersection Local Time." Ann. Probab. 18 (3) 959 - 977, July, 1990. https://doi.org/10.1214/aop/1176990731
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