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)
Viernes 20 de Noviembre 17:30 hrs. Sala 2, Facultad de matemáticas, Campus San Joaquín, Puc Chile.

Department of Mathematics

Pontifical Catholic University of Chile (PUC-Chile)

Av. Vicuña Mackenna 4860, Macul,

Santiago – Chile

(+56 2) 2354 5779

Center for Mathematical Modeling (CMM)

Faculty of Physical and Mathematical Sciences (FCFM)

Universidad de Chile

Beauchef 851, Edificio Norte, Piso 7,

Santiago – Chile