We study the invariance of stochastic differential equations under random
diffeomorphisms, and establish the determining equations for random Lie-point
symmetries of stochastic differential equations, both in Ito and in
Stratonovich form. We also discuss relations with previous results in the
literature.Comment: In new version (November 2017) we have added an important ERRATUM.
Due to a trivial mistake in a formula, several examples should be revised;
more relevant, the qualitatove results of Section VIII turn out to be wrong,
as discussed in the erratum. See also arXiv:1711.0199
