An inductive approach to stochastic estimates for the ${\phi }_2^4$-equation with correlated coefficient field

We develop an inductive approach to obtaining stochastic estimates for the ${\phi }_2^4$-equation when the coefficient field is correlated with the driving noise. Our method is based on (infinite-dimensional) Gaussian integration by parts with respect to Wick products of Gaussian random variables (more precisely, mollifications of space-time white noise)