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Self-intersection local time of planar Brownian motion based on a strong approximation by random walks

Authors
  • Szabados, Tamás
Type
Published Article
Publication Date
Mar 02, 2011
Submission Date
Aug 05, 2010
Identifiers
DOI: 10.1007/s10959-011-0351-x
Source
arXiv
License
Yellow
External links

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.

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