  We build and study a recursive algorithm based on the occupation measure of
an Euler scheme with decreasing step for the numerical approximation of the
quasistationary distribution (QSD) of an elliptic diffusion in a bounded
domain. We prove the almost sure convergence of the procedure for a family of
redistributions and show that we can also recover the approximation of the rate
of survival and the convergence in distribution of the algorithm. This last
point follows from some new bounds on the weak error related to diffusion
dynamics with renewal.
