Gregorio Moreno (PUC Chile)

This work is a first step in the study of the convergence of certain discrete models to SDEs with a distributional drift. In this talk, we analyse the case of a random walk in a one-dimensional evanescent random environment. We show convergence to the Brox diffusion, a diffusion which drift corresponds formally to the derivative of a double-sided Brownian motion.

The main tool is the theory of paracontrolled distributions introduced by Gubinelli-Imkeller&Perkowski, and a characterisation of diffusions with singular drifts by Delarue&Diel, and by Canizzaro&Chouck.