  We prove a convergence result for a large class of random models that
encompasses the case of the BPHZ models used in the study of singular
stochastic PDEs. We introduce for that purpose a useful variation on the notion
of regularity structure called a regularity-integrability structure. It allows
to deal in a single elementary setting with models on a usual regularity
structure and their first order Malliavin derivative.

Probability;Analysis of PDEs