Piecewise linear approximation for the dynamical ${\Phi }_3^4$ model

Abstract

We construct a piecewise linear approximation for the dynamical ${\Phi }_3^4$ model on ${\mathbb{T}}^3$ by the theory of regularity structures in [Hai14]. For the dynamical ${\Phi }_3^4$ model it is proved in [Hai14] that a renormalisation has to be performed in order to define the nonlinear term. Compared to the results in [Hai14] we consider piecewise linear approximations to space-time white noise and prove that the solutions to the approximating equations converge to the solution to the dynamical ${\Phi }_3^4$ model. The renormalisation in this case corresponds to adding the solution multiplied by a function depending on $t$ in the approximating equation.

arXiv admin note: text overlap with arXiv:1303.5113 by other authors

References in corpus (5)

• The dynamical sine-Gordon model
• Approximating three-dimensional Navier-Stokes equations driven by space-time white noise
• Restricted Markov uniqueness for the stochastic quantization of $P(\Phi {)}_2$ and its applications
• Lattice approximation to the dynamical ${\Phi }_3^4$ model
• Three-dimensional Navier-Stokes equations driven by space-time white noise

Cited by in corpus (4)

• Restricted Markov uniqueness for the stochastic quantization of $P(\Phi {)}_2$ and its applications
• Lattice approximation to the dynamical ${\Phi }_3^4$ model
• An introduction to singular SPDEs
• Convergence rate for Galerkin approximation of the stochastic Allen-Cahn equations on 2D torus