A stochastic approximation approach to quasi-stationary distributions on finite spaces

Abstract

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.

References in corpus (3)

• A survey of random processes with reinforcement
• Quasi-stationary distributions and population processes
• Theoretical analysis of a Stochastic Approximation approach for computing Quasi-Stationary distributions

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• Uniform in time propagation of chaos for a Moran model
• Quasi-stationary distributions in reducible state spaces
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