Bogoliubov-type recursions for renormalisation in regularity structures

  • Yvain Bruned

    IECL (UMR 7502), Universite de Lorraine, Vandœuvre-lès-Nancy, France
  • Kurusch Ebrahimi-Fard

    Norwegian University of Science and Technology (NTNU), Trondheim, Norway
Bogoliubov-type recursions for renormalisation in regularity structures cover
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Abstract

Hairer's regularity structures transformed the theory of singular stochastic partial differential equations and their solutions. 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.

Cite this article

Yvain Bruned, Kurusch Ebrahimi-Fard, Bogoliubov-type recursions for renormalisation in regularity structures. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 12 (2025), no. 4, pp. 673–703

DOI 10.4171/AIHPD/186