Paracontrolled calculus and FunakiQuastel approximation for the KPZ equation
Abstract
In this paper, we consider the approximating KPZ equation introduced by Funaki and Quastel [2], which is suitable for studying invariant measures. They showed that the stationary solution of the approximating equation converges to the ColeHopf solution of the KPZ equation with extra term $(1/24)t$. On the other hand, Gubinelli and Perkowski [5] gave a pathwise meaning to the KPZ equation as an application of the paracontrolled calculus. We show that Funaki and Quastel's result is extended to nonstationary solutions by using the paracontrolled calculus.
 Publication:

arXiv eprints
 Pub Date:
 May 2016
 DOI:
 10.48550/arXiv.1605.02624
 arXiv:
 arXiv:1605.02624
 Bibcode:
 2016arXiv160502624H
 Keywords:

 Mathematics  Probability;
 35R60;
 60H15;
 60H40
 EPrint:
 52 pages, modified arguments