QUASI-STATIONARY DISTRIBUTIONS FOR STOCHASTIC APPROXIMATION ALGORITHMS WITH CONSTANT STEP SIZE

Bastien Marmet (1)

1 UNINE - Institut de Mathématiques

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.

Mots clés: Stochastic Approximation Algorithm; Quasi-Stationary Distributions

Domaines: Probabilités [math.PR]

Bastien Marmet. QUASI-STATIONARY DISTRIBUTIONS FOR STOCHASTIC APPROXIMATION ALGORITHMS WITH CONSTANT STEP SIZE. 2012. ⟨hal-00805201⟩