Open Access
2015 A stochastic approximation approach to quasi-stationary distributions on finite spaces
Michel Benaïm, Bertrand Cloez
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Electron. Commun. Probab. 20: 1-13 (2015). DOI: 10.1214/ECP.v20-3956


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 methodintroduced 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 somedeterministic dynamical system induced by a vector field on the unit simplex. This approach provides new proof of convergence as well as precise asymptotic rates for this type of algorithm. Inthe last part, our convergence results are compared with those of a particle system algorithm (adiscrete-time version of the Fleming-Viot algorithm).


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Michel Benaïm. Bertrand Cloez. "A stochastic approximation approach to quasi-stationary distributions on finite spaces." Electron. Commun. Probab. 20 1 - 13, 2015.


Accepted: 12 May 2015; Published: 2015
First available in Project Euclid: 7 June 2016

zbMATH: 1321.65009
MathSciNet: MR3352332
Digital Object Identifier: 10.1214/ECP.v20-3956

Primary: 60B12 , 60J10 , 65C20
Secondary: 34F05 , 60J20

Keywords: approximation method , Quasi-stationary distributions , random perturbations of dynamical , reinforced random walks

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