Lattice approximation to the dynamical .43 model

We study the lattice approximations to the dynamical .43 model by paracontrolled distributions proposed in [Forum Math. Pi 3 (2015) e6]. We prove that the solutions to the lattice systems converge to the solution to the dynamical .43 model in probability, locally uniformly in time. Since the dynamical .43 model is not well defined in the classical sense and renormalisation has to be performed in order to define the nonlinear term, a corresponding suitable drift term is added in the stochastic equations for the lattice systems.