Donsker's theorem in {Wasserstein}-1 distance
Abstract
We compute the Wassertein-1 (or Kantorovitch-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.
Domains
Probability [math.PR]
Fichier principal
donskerLipschitz.pdf (180.03 Ko)
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lipschitz_slides.pdf (1.72 Mo)
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