## Marchal, Philippe - 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.

Volume: DMTCS Proceedings vol. AC, Discrete Random Walks (DRW'03)
Section: Proceedings
Published on: January 1, 2003
Submitted on: May 10, 2017
Keywords: strong convergence,simple random walk,Brownian motion,[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]