Abstract
For non-homogeneous Markov chains (nhmc), the Markov property is retained but the transition probabilities may depend on time. This section gives conditions guaranteeing the existence of a limit in variation of such chains, with their application to simulated annealing in view. When the state space E is finite and the chain is ergodic, Dobrushin’s ergodic coefficient (Subsection 4.3.4) is the basic tool to obtain a necessary and sufficient condition of weak ergodicity (yet to be defined) of non-homogeneous Markov chains.
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Brémaud, P. (2020). Non-homogeneous Markov Chains. In: Markov Chains. Texts in Applied Mathematics, vol 31. Springer, Cham. https://doi.org/10.1007/978-3-030-45982-6_12
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DOI: https://doi.org/10.1007/978-3-030-45982-6_12
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Publisher Name: Springer, Cham
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Online ISBN: 978-3-030-45982-6
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