Recursive formulae in regularity structures

TL;DR

This paper introduces a recursive approach to constructing renormalised models within regularity structures, streamlining the renormalisation process for singular SPDEs and extending previous algebraic methods.

Contribution

It develops a recursive formulation for the structure and renormalisation groups, enhancing the existing Hopf algebra-based renormalisation techniques in regularity structures.

Findings

Unified recursive construction for models and renormalisation groups

Applicable to all known singular SPDEs treated with regularity structures

Improves efficiency and generality of renormalisation procedures

Abstract

We construct renormalised models of regularity structures by using a recursive formulation for the structure group and for the renormalisation group. This construction covers all the examples of singular SPDEs which have been treated so far with the theory of regularity structures and improves the renormalisation procedure based on Hopf algebras given in [BHZ16].