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Constructing a sequence of random walks strongly converging to Brownian motion

Abstract : 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.
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Philippe Marchal. Constructing a sequence of random walks strongly converging to Brownian motion. Discrete Random Walks, DRW'03, 2003, Paris, France. pp.181-190. ⟨hal-01183930⟩

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