Markov Chains pp 399-422 | Cite as

Non-homogeneous Markov Chains

  • Pierre Brémaud
Part of the Texts in Applied Mathematics book series (TAM, volume 31)


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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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Pierre Brémaud
    • 1
  1. 1.ParisFrance

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