Part of the Universitext book series (UTX)
Convergence of Markov Chains
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
that the chain does not leave
or that are visited by the chain periodically; e.g., only for odd n or only for even n.
KeywordsMarkov Chain Random Walk Transition Matrix Ising Model Gibbs Sampler
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© Springer-Verlag London Limited 2008