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 Electronic Journal of Probability > Vol. 10 (2005) > Paper 4 open journal systems 


An Almost Sure Invariance Principle for Renormalized Intersection Local Times

Richard F. Bass, University of Connecticut, USA
Jay Rosen, City University of New York, USA


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.


Full text: PDF

Pages: 124-164

Published on: February 28, 2005
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Electronic Journal of Probability. ISSN: 1083-6489