Non-homogeneous Markov Chains
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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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