Discretisation of regularity structures

Abstract

We introduce a general framework allowing to apply the theory of regularity structures to discretisations of stochastic PDEs. The approach pursued in this article is that we do not focus on any one specific discretisation procedure. Instead, we assume that we are given a scale $\epsilon >0$ and a "black box" describing the behaviour of our discretised objects at scales below $\epsilon$.

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• KPZ reloaded
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• A central limit theorem for the KPZ equation
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Cited by in corpus (7)

• Geometric stochastic heat equations
• Log-Sobolev inequality for the continuum sine-Gordon model
• Some recent progress in singular stochastic PDEs
• Martingale-driven approximations of singular stochastic PDEs
• Large-scale limit of interface fluctuation models
• Stochastic quantization of an Abelian gauge theory
• The ${\Phi }_3^4$ measure has sub-Gaussian tails