  We consider the stability problems of one dimensional SDEs when the diffusion
coefficients satisfy the so called Nakao-Le Gall condition. The explicit rate
of convergence of the stability problems are given by the Yamada-Watanabe
method without the drifts. We also discuss the convergence rate for the SDEs
driven by the symmetric $\alpha$ stable process. These stability rate problems
are extended to the case where the drift coefficients are bounded and in $L^1$.
It is shown that the convergence rate is invariant under the removal of drift
method for the SDEs driven by the Wiener process.
