Bogoliubov type recursions for renormalisation in regularity structures

Yvain Bruned, Kurusch Ebrahimi-Fard

Research output: Working paper

Abstract

Hairer’s regularity structures transformed the solution theory of singular stochastic partial differential equations. The notions of positive and negative renormalisation are central and the intricate interplay between these two renormalisation procedures is captured through the combination of cointeracting bialgebras and an algebraic Birkhoff-type decomposition of bialgebra morphisms. This work revisits the latter by defining Bogoliubov-type recursions similar to Connes and Kreimer’s formulation of BPHZ renormalisation. We then apply our approach to the renormalisation problem for SPDEs as well as the proposal for resonance based numerical schemes for certain partial differential equations in numerical analysis introduced in a recent work by the first author.
Original languageEnglish
PublisherArXiv
Number of pages31
Publication statusPublished - 11 Jun 2020

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