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2005 An Almost Sure Invariance Principle for Renormalized Intersection Local Times
Richard Bass, Jay Rosen
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Electron. J. Probab. 10: 124-164 (2005). DOI: 10.1214/EJP.v10-236

Abstract

Let $\beta_k(n)$ be the number of self-intersections of order $k$, appropriately renormalized, for a mean zero planar random walk with $2+\delta$ moments. On a suitable probability space we can construct the random walk and a planar Brownian motion $W_t$ such that for each $k \geq 2$, $|\beta_k(n)- \gamma_k(n)|=o(1)$, a.s., where $\gamma_k(n)$ is the renormalized self-intersection local time of order $k$ at time 1 for the Brownian motion $W_{nt}/\sqrt n$.

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Richard Bass. Jay Rosen. "An Almost Sure Invariance Principle for Renormalized Intersection Local Times." Electron. J. Probab. 10 124 - 164, 2005. https://doi.org/10.1214/EJP.v10-236

Information

Accepted: 28 February 2005; Published: 2005
First available in Project Euclid: 1 June 2016

zbMATH: 1084.60021
MathSciNet: MR2120241
Digital Object Identifier: 10.1214/EJP.v10-236

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