  Symmetries can be used to integrate scalar Ito equation -- or reduce systems
of such equations -- by the Kozlov substitution, i.e. passing to symmetry
adapted coordinates. While the theory is well established for so called
deterministic standard symmetries (the class originally studied by Kozlov),
some points need clarification for so called random standard symmetries and
W-symmetries. This paper is devoted to such clarification; in particular we
note that the theory naturally calls, for these classes of symmetries, to also
consider generalized Ito equations; and that while Kozlov theory is extended
substantially unharmed for random standard symmetries, W-symmetries should be
handled with great care, and cannot be used towards integration of stochastic
equations, albeit they have different uses.
