Existence and asymptotic behaviour of some time-inhomogeneous diffusions (Q1943325)

A scalar diffusion with a time-dependent drift of the form \(\rho \operatorname{sgn}(x)|x|^{\alpha}/t^{\beta}\) that is the subgradient of a certain potential, is analyzed for various values of the parameters \(\rho, \alpha, \beta\) and the initial data. The results include existence and uniqueness of path-wise or weak solutions, conditions for explosion and non-explosion, transience and recurrence in a suitable sense, and limit theorems, both distributional and almost sure ones, for suitable scalings.