Quasi-Stationary Distributions for Stochastic Approximation Algorithms with constant step size

Abstract: In this paper we investigate quasi-stationary distributions {\mu}_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 {\mu}_N are invariant measures for the ODE with support in the interior attractors.