  We consider driftless stochastic differential equations and the diffusions
starting from the positive half line. It is shown that the Feller test for
explosions gives a necessary and sufficient condition to hold pathwise
uniqueness for diffusion coefficients that are positive and monotonically
increasing or decreasing on the positive half line and the value at the origin
is zero. Then, stability problems are studied from the aspect of
H\"older-continuity and a generalized Nakao-Le Gall condition. Comparing the
convergence rate of H\"older-continuous case, the sharpness and stability of
the Nakao-Le Gall condition on Cantor stochastic differential equations is
confirmed.Furthermore, using the Malliavin calculus, we construct a smooth
solution to degenerate second order Fokker-Planck equations under weak
conditions on the coefficients.
