September 2016 Analysis of a stochastic approximation algorithm for computing quasi-stationary distributions
J. Blanchet, P. Glynn, S. Zheng
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Adv. in Appl. Probab. 48(3): 792-811 (September 2016).

Abstract

We study the convergence properties of a Monte Carlo estimator proposed in the physics literature to compute the quasi-stationary distribution on a transient set of a Markov chain (see De Oliveira and Dickman (2005), (2006), and Dickman and Vidigal (2002)). Using the theory of stochastic approximations we verify the consistency of the estimator and obtain an associated central limit theorem. We provide an example showing that convergence might occur very slowly if a certain eigenvalue condition is violated. We alleviate this problem using an easy-to-implement projection step combined with averaging.

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J. Blanchet. P. Glynn. S. Zheng. "Analysis of a stochastic approximation algorithm for computing quasi-stationary distributions." Adv. in Appl. Probab. 48 (3) 792 - 811, September 2016.

Information

Published: September 2016
First available in Project Euclid: 19 September 2016

zbMATH: 1352.60106
MathSciNet: MR3568892

Subjects:
Primary: 60J22
Secondary: 60J10

Keywords: central limit theorem , Markov chain , quasi-stationary distribution , stochastic approximation

Rights: Copyright © 2016 Applied Probability Trust

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Vol.48 • No. 3 • September 2016
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