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Introduction to general state-space Markov chain theory. (English) Zbl 0849.60072
Gilks, W. R. (ed.) et al., Markov chain Monte Carlo in practice. London: Chapman & Hall. 59-74 (1996).
This paper summarizes some of the results of general state-space Markov chain theory as Nummelin, and Meyn and Tweedie applied to Markov chain Monte Carlo samplers. The distinguishing feature of these samplers used is that they are known by construction to have a particular distribution as an invariant distribution. Many results are analogous to results for discrete state-space chain, but there are some differences which are illustrated by a simple random walk example.
MSC:
60J10Markov chains (discrete-time Markov processes on discrete state spaces)
65C05Monte Carlo methods
60G50Sums of independent random variables; random walks