Piecewise linear approximation for the dynamical Φ34 model

We construct a piecewise linear approximation for the dynamical Φ34 model on T³. The approximation is based on the theory of regularity structures developed by Hairer (2014). They proved that renormalization in a dynamical Φ34 model is necessary for defining the nonlinear term. In contrast to Hairer (2014), we apply piecewise linear approximations to space-time white noise, and prove that the solutions of the approximating equations converge to the solution of the dynamical Φ34 model. In this case, the renormalization corresponds to multiplying the solution by a t-dependent function, and adding it to the approximating equation.