Renormalisation in the flow approach for singular SPDEs

Abstract: In this work, we study the renormalisation of singular SPDEs in the flow approach recently developed by Duch using a bottom-up setting. We introduce a general ansatz based on decorated trees for the solution of the flow equation. The ansatz is renormalised in a recursive way, in the sense of the trees, via local extractions introduced for regularity structures. We derive the renormalised equation from this ansatz and show that the renormalisation scheme is identical to that appearing in the context of regularity structures, thus matching the BPHZ renormalisation.