The ODE method for some self-interacting diffusions on ℝd
The aim of this paper is to study the long-term behavior of a class of self-interacting diffusion processes on ℝ. These are solutions to SDEs with a drift term depending on the actual position of the process and its normalized occupation measure . These processes have so far been studied on compact spaces by Benaïm, Ledoux and Raimond, using stochastic approximation methods. We extend these methods to ℝ, assuming a confinement potential satisfying some conditions. These hypotheses...