DISCRETISATIONS OF ROUGH STOCHASTIC PDES

• 成果类型: Article
• 署名作者: Hairer, M.; Matetski, K.
• 署名单位: Imperial College London; University of Toronto
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/17-AOP1212
• 发表日期: 2018
• 页码: 1651-1709
• 关键词: classical statistical-mechanics; quantum field-theory; differential-equations; finite-volume; QUANTIZATION; CONVERGENCE; MODEL

摘要

We develop a general framework for spatial discretisations of parabolic stochastic PDEs whose solutions are provided in the framework of the theory of regularity structures and which are functions in time. As an application, we show that the dynamical Phi(4)(3) model on the dyadic grid converges after renormalisation to its continuous counterpart. This result in particular implies that, as expected, the Phi(4)(3) measure with a sufficiently small coupling constant is invariant for this equation and that the lifetime of its solutions is almost surely infinite for almost every initial condition.