Analysis of a stochastic approximation algorithm for computing quasi-stationary distributions
2016 ◽
Vol 48
(3)
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pp. 792-811
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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.
2009 ◽
Vol 14
(0)
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pp. 2130-2155
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2015 ◽
Vol 25
(1)
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pp. 211-234
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1992 ◽
Vol 41
(1)
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pp. 33-44
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1998 ◽
Vol 35
(01)
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pp. 1-11
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Keyword(s):
2012 ◽
Vol 21
(5)
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pp. 715-733
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Keyword(s):
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2012 ◽
Vol 33
(1)
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pp. 73-82
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