Self-intersection Local Time of Planar Brownian Motion Based on a Strong Approximation by Random Walks

Tamás Szabados ()
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Tamás Szabados: Budapest University of Technology and Economics

Journal of Theoretical Probability, 2012, vol. 25, issue 4, 1081-1118

Abstract: Abstract The main purpose of this work is to define planar self-intersection local time by an alternative approach which is based on an almost sure pathwise approximation of planar Brownian motion by simple, symmetric random walks. As a result, Brownian self-intersection local time is obtained as an almost sure limit of local averages of simple random walk self-intersection local times. An important tool is a discrete version of the Tanaka–Rosen–Yor formula; the continuous version of the formula is obtained as an almost sure limit of the discrete version. The author hopes that this approach to self-intersection local time is more transparent and elementary than other existing ones.

Keywords: Self-intersection local time; Strong approximation; Random walk; Ito’s formula; Tanaka–Rosen–Yor formula; 60J55; 60F15; 60G50 (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10959-011-0351-x

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