Lattice approximation to the dynamical $\phi_{3}^{4}$ model
Zhu, Rongchan
Zhu, Xiangchan
Phi(4)(3) model
regularity structure
paracontrolled distribution
space-time white noise
renormalisation
We study the lattice approximations to the dynamical Phi(4)(3) 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 Phi(4)(3) model in probability, locally uniformly in time. Since the dynamical Phi(4)(3) 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.
Inst Mathematical Statistics
2018
info:eu-repo/semantics/article
doc-type:article
text
https://pub.uni-bielefeld.de/record/2920359
Zhu R, Zhu X. Lattice approximation to the dynamical $\phi_{3}^{4}$ model. <em>The Annals of Probability</em>. 2018;46(1):397-455.
eng
info:eu-repo/semantics/altIdentifier/doi/10.1214/17-AOP1188
info:eu-repo/semantics/altIdentifier/issn/0091-1798
info:eu-repo/semantics/altIdentifier/wos/000430921800009
info:eu-repo/semantics/closedAccess