Marchal, Philippe
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Constructing a sequence of random walks strongly converging to Brownian motion
dmtcs:3335 -
Discrete Mathematics & Theoretical Computer Science,
January 1, 2003,
DMTCS Proceedings vol. AC, Discrete Random Walks (DRW'03)
Constructing a sequence of random walks strongly converging to Brownian motion
Authors: Marchal, Philippe
We give an algorithm which constructs recursively a sequence of simple random walks on $\mathbb{Z}$ 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.