Space-time discrete KPZ equation
Probability
2018-01-11 v2 Mathematical Physics
math.MP
Abstract
We study a general family of space-time discretizations of the KPZ equation and show that they converge to its solution. The approach we follow makes use of basic elements of the theory of regularity structures [M. Hairer, A theory of regularity structures, Invent. Math. 2014] as well as its discrete counterpart [M. Hairer, K. Matetski, Discretizations of rough stochastic PDEs, 2015]. Since the discretization is in both space and time and we allow non-standard discretization for the product, the methods mentioned above have to be suitably modified in order to accommodate the structure of the models under study.
Cite
@article{arxiv.1611.09719,
title = {Space-time discrete KPZ equation},
author = {Giuseppe Cannizzaro and Konstantin Matetski},
journal= {arXiv preprint arXiv:1611.09719},
year = {2018}
}