We consider a Markov chain X with invariant distribution π and investigate conditions under which the distribution of X n converges to π for n → ∞. Essentially it is necessary and sufficient that the state space of the chain cannot be decomposed into subspaces
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that the chain does not leave
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or that are visited by the chain periodically; e.g., only for odd n or only for even n.
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© 2008 Springer-Verlag London Limited
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(2008). Convergence of Markov Chains. In: Probability Theory. Universitext. Springer, London. https://doi.org/10.1007/978-1-84800-048-3_18
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DOI: https://doi.org/10.1007/978-1-84800-048-3_18
Publisher Name: Springer, London
Print ISBN: 978-1-84800-047-6
Online ISBN: 978-1-84800-048-3
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