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.

Joint work with Manuel Cabezas (PUC)


Departamento de Matemáticas

Pontificia Universidad Católica de Chile (PUC-Chile)

Av. Vicuña Mackenna 4860, Macul,

Santiago – Chile

(+56 2) 2354 5779

Centro de Modelamiento Matemático (CMM)

Facultad de Ciencias Físicas y Matemáticas (FCFM)

Universidad de Chile

Beauchef 851, Edificio Norte, Piso 7,

Santiago – Chile