W-Symmetries of Ito stochastic differential equations

We discuss W-symmetries of Ito stochastic differential equations, introduced in a recent paper by Gaeta and Spadaro [J. Math. Phys. 2017]. In particular, we discuss the general form of acceptable generators for continuous (Lie-point) W-symmetry, arguing they are related to the (linear) conformal group, and how W-symmetries can be used in the integration of Ito stochastic equations along Kozlov theory for standard (deterministic or random) symmetries. It turns out this requires, in general, to consider more general classes of stochastic equations than just Ito ones.