Abstract
All dynamic Monte Carlo algorithms have three properties in common: (i) A given configuration is updated in subsequent steps. (ii) Each step is governed by some probabilistic rule. (iii) This rule depends only on the number of the step and on the present configuration. The state of such a system evolves according to some random dynamics without memory. The theory of Markov chains is the proper framework to study such random evolutions. In this chapter, Markov chains are introduced and their asymptotic behaviour is examined. The abstract limit theorems will be applied later to various dynamic Monte Carlo methods.
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© 2003 Springer-Verlag Berlin Heidelberg
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Winkler, G. (2003). Markov Chains: Limit Theorems. In: Image Analysis, Random Fields and Markov Chain Monte Carlo Methods. Applications of Mathematics, vol 27. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55760-6_5
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DOI: https://doi.org/10.1007/978-3-642-55760-6_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-62911-2
Online ISBN: 978-3-642-55760-6
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