  This paper studies a method, which has been proposed in the Physics
literature by [8, 7, 10], for estimating the quasi-stationary distribution. In
contrast to existing methods in eigenvector estimation, the method eliminates
the need for explicit transition matrix manipulation to extract the principal
eigenvector. Our paper analyzes the algorithm by casting it as a stochastic
approximation algorithm (Robbins-Monro) [23, 16]. In doing so, we prove its
convergence and obtain its rate of convergence. Based on this insight, we also
give an example where the rate of convergence is very slow. This problem can be
alleviated by using an improved version of the algorithm that is given in this
paper. Numerical experiments are described that demonstrate the effectiveness
of this improved method.
