M. Gubinelli, N. Perkowski
Published 2015-08-31Version 1
Energy solutions is a weak notion of solution to the KPZ equation which was introduced by Gon\c{c}alves and Jara [ARMA 212 (2013)] to describe the large scale fluctuations of a wide class of weakly asymmetric particle systems. In this paper we prove that energy solutions of the periodic, stationary, stochastic Burgers equation are unique and in particular they coincide with the Hopf--Cole solution. To obtain uniqueness we use the reformulation of the energy solution concept given by Gubinelli and Jara [SPDE--AC 1 (2013)] and an observation by Funaki and Quastel [ArXiv:1407.7310].
Wick Product in The Stochastic Burgers Equation: A Curse or a Cure?
A stochastic Burgers equation from a class of microscopic interactions
Gaussian Fluctuations for the stochastic Burgers equation in dimension $d\geq 2$
![QR code for arXiv:1508.07764 [math.PR]](http://oss.arxitics.com/images/favicon.svg)