Lattice approximation to the dynamical Φ43Φ34 model

Rongchan Zhu ^[1] ; Xiangchan Zhu ^[2]
1. [1] Beijing Institute of Technology
  
  Beijing Institute of Technology
  
  China
2. [2] Beijing Jiaotong University
  
  Beijing Jiaotong University
  
  China
Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 46, Nº. 1, 2018, págs. 397-455
Idioma: inglés
DOI: 10.1214/17-AOP1188
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Resumen
- We study the lattice approximations to the dynamical Φ43Φ34 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 Φ43Φ34 model in probability, locally uniformly in time. Since the dynamical Φ43Φ34 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.