Discrete Random Walks, DRW'03
Cyril Banderier and Christian Krattenthaler (eds.)
DMTCS Conference Volume AC (2003), pp. 181190
author:  Philippe Marchal 

title:  Constructing a sequence of random walks strongly converging to Brownian motion 
keywords:  strong convergence, simple random walk, Brownian motion 
abstract: 
We give an algorithm which constructs recursively a
sequence of simple random walks on
Z
converging almost surely to a Brownian motion. One
obtains by the same method conditional versions of the
simple random walk converging to the excursion, the bridge,
the meander or the normalized pseudobridge.

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reference:  Philippe Marchal (2003), Constructing a sequence of random walks strongly converging to Brownian motion, in Discrete Random Walks, DRW'03, Cyril Banderier and Christian Krattenthaler (eds.), Discrete Mathematics and Theoretical Computer Science Proceedings AC, pp. 181190 
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