English

Paracontrolled calculus and Funaki-Quastel approximation for the KPZ equation

Probability 2017-02-28 v3

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 Cole-Hopf solution of the KPZ equation with extra term (1/24)t(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.

Keywords

Cite

@article{arxiv.1605.02624,
  title  = {Paracontrolled calculus and Funaki-Quastel approximation for the KPZ equation},
  author = {Masato Hoshino},
  journal= {arXiv preprint arXiv:1605.02624},
  year   = {2017}
}

Comments

52 pages, modified arguments