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  1. Home > Articles & Issues >
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  3. Constructing a seque ...
Conference paper

Constructing a sequence of random walks strongly converging to Brownian motion

Philippe Marchal (1)
(1) École normale supérieure - Paris
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Imported on
May 10, 2017
Published on
December 31, 2002
Last modified on
March 31, 2025
Volume 0
DMTCS Proceedings vol. AC, Discrete Random Walks (DRW'03)
Proceedings
DOI
10.46298/dmtcs.3335
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https://about.hal.science/hal-authorisation-v1
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Constructing a sequence of random walks strongly converging to Brownian motion

Philippe Marchal (1)
(1) École normale supérieure - Paris
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.
Keywords
  • [INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS]
  • [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
  • [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
  • [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG]
  • strong convergence
  • simple random walk
  • Brownian motion
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