Corpus ID: 119660671

Order of magnitude time-reversible Markov chains and characterization of clustering processes

@article{Joshi2011OrderOM,
  title={Order of magnitude time-reversible Markov chains and characterization of clustering processes},
  author={Badal Joshi},
  journal={arXiv: Probability},
  year={2011}
}
We introduce the notion of order of magnitude reversibility (OM-reversibility) in Markov chains that are parametrized by a positive parameter $\ep$. OM-reversibility is a weaker condition than reversibility, and requires only the knowledge of order of magnitude of the transition probabilities. For an irreducible, OM-reversible Markov chain on a finite state space, we prove that the stationary distribution satisfies order of magnitude detailed balance (analog of detailed balance in reversible… Expand

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