Analysis of a stochastic approximation algorithm for computing quasi-stationary distributions

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 approximati...

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Vydáno v:Advances in applied probability Ročník 48; číslo 3; s. 792 - 811
Hlavní autoři: Blanchet, J., Glynn, P., Zheng, S.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Cambridge, UK Cambridge University Press 01.09.2016
Applied Probability Trust
Témata:
Approximation
Central limit theorem
Computer simulation
Consistency
Convergence
Eigenvalues
Estimators
Markov analysis
Markov chains
Mathematical analysis
Probability
Projection
Stochasticity
Markov chain
Quasi-stationary distribution
central limit theorem
Primary 60J22
stochastic approximation
Secondary 60J10
ISSN:0001-8678, 1475-6064
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Shrnutí: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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ISSN:0001-8678
1475-6064
DOI:10.1017/apr.2016.28