Symmetries for the gKPZ equation via multi-indices

In this talk, I will present how to use the recent theory multi-indices to compute the dimension of the two spaces associated with the symmetries of the one-dimensional generalised KPZ equation (gKPZ): the chain rule and the Itˆo Isometry. 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.

Joint work with Y. Bruned (Université de Lorraine).