Stability for Temporally Nonhomogeneous Singular Diffusion

The stability results given in Has'minskii [6] (pp.90-91) do not work, in general, even for temporally homogeneous singular diffusions; we will explain this with an example at the end. First we present some criteria for asymptotic flatness for a temporally nonhomogeneous singular diffusion and these results generalize the main result in Basak and Bhattacharya [1] and a result in Basak [2]. Next we specialize these criteria to the homogeneous case and obtain a general result on stability for homogeneous singular diffusions.