A finite-energy bound on the approach of a diffusion to the zeros of its density
Timothy C. Wallstrom · Proceedings of the American Mathematical Society · 1990
Since the drift coefficients of a finite-energy diffusion are undefined on the nodes, or zeros of the density, an important problem has been to show that the sample paths stay away from the nodes. In this paper it is shown that if the drift is locally a gradient and smooth on the complement of the nodes, and if the density is smooth, then the closest approach to the nodes can be bounded solely in terms of the time-integrated energy.