Donsker's theorem in {Wasserstein}-1 distance

Published 15 Apr 2019 in math.PR | (1904.07045v1)

Abstract: We compute the Wassertein-1 (or Kolmogorov-Rubinstein) distance between a random walk in $R^d$ and the Brownian motion. The proof is based on a new estimate of the Lipschitz modulus 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.

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