In this work, we approximate a diffusion process by its Euler scheme and we study the convergence of the density of the marginal laws. We improve previous estimates especially for small time.
"Sharp estimates for the convergence of the density of the Euler scheme in small time." Electron. Commun. Probab. 13 352 - 363, 2008. https://doi.org/10.1214/ECP.v13-1393