Pathwise optimal transport bounds between a one-dimensional diffusion and its Euler scheme

@inproceedings{Alfonsi2012PathwiseOT,
  title={Pathwise optimal transport bounds between a one-dimensional diffusion and its Euler scheme},
  author={Aur{\'e}lien Alfonsi and Benjamin Jourdain and Arturo Kohatsu-Higa},
  year={2012}
}
In the present paper, we prove that the Wasserstein distance on the space of continuous sample-paths equipped with the supremum norm between the laws of a uniformly elliptic one-dimensional diffusion process and its Euler discretization with N steps is smaller than O(N) where ε is an arbitrary positive constant. This rate is intermediate between the strong error estimation in O(N) obtained when coupling the stochastic differential equation and the Euler scheme with the same Brownian motion and… CONTINUE READING