Symmetries for the gKPZ equation via multi‐indices

Abstract In this work, we study the two main symmetries for the one‐dimensional generalised KPZ equation (gKPZ): the chain rule and the Itô isometry. We consider the equation in the full subcritical regime and use multi‐indices that avoid an over‐parametrisation of the renormalised equation to compute the dimension of the two spaces associated with these two symmetries. Our proof is quite elementary and shows that multi‐indices provide in this case a simplification in comparison to the results obtained via decorated trees. It also completes the program on the study of the chain rules iniated first for space‐time white noise and continued for the subcritical regime with decorated trees.