Perturbation theory for Markov chains via Wasserstein distance

@article{Rudolf2015PerturbationTF,
  title={Perturbation theory for Markov chains via Wasserstein distance},
  author={Daniel Rudolf and Nikolaus Schweizer},
  journal={arXiv: Computation},
  year={2015}
}
Perturbation theory for Markov chains addresses the question how small differences in the transitions of Markov chains are reflected in differences between their distributions. We prove powerful and flexible bounds on the distance of the $n$th step distributions of two Markov chains when one of them satisfies a Wasserstein ergodicity condition. Our work is motivated by the recent interest in approximate Markov chain Monte Carlo (MCMC) methods in the analysis of big data sets. By using an… Expand

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