Boundedness and convergence of some self-attracting diffusionsMathematische Annalen - Tập 325 - Trang 81-96 - 2003
Samuel Herrmann, Bernard Roynette
We consider some self-attracting diffusions and study the behaviour of their paths when time tends to infinity. We prove that, in case the interaction is nonlocal, the paths are bounded a.s. even if they don't converge. Otherwise, we generalize the convergence result of M. Cranston and Y. Le Jan.