arXiv subjects
Publications and source records attributed to Bastien Marmet.
In this paper we investigate the long time behavior of a family of diffusion processes with Hölder continuous diffusion terms on a compact set, these process arise naturally in random approximations of an ODE. We will prove that these processes hit the boundary in finite time and prove the existence of a quasi-stationnary distribution
In this paper we investigate quasi-stationary distributions μ_N of stochastic approximation algorithms with constant step size which can be viewed as random perturbations of a time-continuous dynamical system. Inspired by ecological models these processes have a closed absorbing set corresponding to extinction. Under some large deviation assumptions and the existence of an interior attractor for the ODE, we show that the weak* limit points of the QSD μ_N are invariant measures for the ODE with support in the interior attractors.