  Symmetry methods are by now recognized as one of the main tools to attack
deterministic differential equations (both ODEs and PDEs); the situation is
quite different for what concerns stochastic differential equations: here,
symmetry considerations are of course quite widely used by theoretical
physicists, but a rigorous and general theory comparable to the one developed
for deterministic equation is still lacking.
  In the following I will report on some work I have done on symmetries of
stochastic (Ito) equations, and how these compare with the symmetries of the
associated diffusion (Fokker-Planck) equations.
