In this paper, we consider the approximating KPZ equation introduced by Funaki and Quastel (2015), 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 [Formula presented]t. On the other hand, Gubinelli and Perkowski (2017) 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.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Modelling and Simulation
- Applied Mathematics