Abstract
We compute the Wassertein-1 (or Kantorovitch-Rubinstein) distance between a random walk in $\mathbf{R} ^{d}$ and the Brownian motion. The proof is based on a new estimate of the modulus of continuity of the solution of the Stein’s equation. As an application, we can evaluate the rate of convergence towards the local time at 0 of the Brownian motion and to a Brownian bridge.
Citation
Laure Coutin. Laurent Decreusefond. "Donsker’s theorem in Wasserstein-1 distance." Electron. Commun. Probab. 25 1 - 13, 2020. https://doi.org/10.1214/20-ECP308
Information