  This work is concerned with the analysis of a stochastic approximation
algorithm for the simulation of quasi-stationary distributions on finite state
spaces. This is a generalization of a method introduced by Aldous, Flannery and
Palacios. It is shown that the asymptotic behavior of the empirical occupation
measure of this process is precisely related to the asymptotic behavior of some
deterministic dynamical system induced by a vector field on the unit simplex.
This approach provides new proof of convergence as well as precise rates for
this type of algorithm. We then compare this algorithm with particle system
algorithms.
