Malliavin calculus and densities for singular stochastic partial differential equations

Abstract We study Malliavin differentiability of solutions to sub-critical singular parabolic stochastic partial differential equations (SPDEs) and we prove the existence densities for a class SPDEs. Both these results are implemented in setting regularity structures. For this construct renormalized models situations where some driving noises replaced by deterministic Cameron–Martin functions, show Lipschitz continuity with respect norm. In particular, many interesting obtain convergence stability result lifts $$L^2$$ L 2 -functions models, which is independent interest. The proof also involves two separate algebraic extensions structure carried out rather large generality.