Analysis of a stochastic approximation algorithm for computing quasi-stationary distributions. (September 2016)

• Record Type: Journal Article
• Authors: Blanchet, J.; Glynn, P.; Zheng, S.
• Is Part Of: Advances in applied probability. Volume 48:Number 3(2016)
• Page Start: 792
• Page End: 811
• Publication Date: 2016-09
• Subjects: Quasi-stationary distribution, -- stochastic approximation, -- Markov chain, -- central limit theorem; Primary 60J22, -- Secondary 60J10; Probabilities -- Periodicals; Stochastic models -- Periodicals; Electronic journals; Periodicals; 519.2
• DOI: 10.1017/apr.2016.28
• Languages: English
• ISSNs: 0001-8678

Abstract

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.