An Almost Sure Invariance Principle for Renormalized Intersection Local Times

Abstract

Let β̃k(n) be the number of self-intersections of order k, appropriately renormalized, for a mean zero random walk Xn in Z with 2 + δ moments. On a suitable probability space we can construct Xn and a planar Brownian motion Wt such that for each k ≥ 2 |β̃k(n)− γ̃k(n)| = O(n−a), a.s. for some a > 0 where γ̃k(n) is the renormalized self-intersection local… (More)

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Cite this paper

@inproceedings{BassAnAS, title={An Almost Sure Invariance Principle for Renormalized Intersection Local Times}, author={Richard F. Bass and Jay Rosen} }