Quantitative bounds for Markov chain convergence: Wasserstein and total variation distances

@article{Madras2010QuantitativeBF,
  title={Quantitative bounds for Markov chain convergence: Wasserstein and total variation distances},
  author={Neal Madras and Deniz Sezer},
  journal={Bernoulli},
  year={2010},
  volume={16},
  pages={882-908}
}
We present a framework for obtaining explicit bounds on the rate of convergence to equilibrium of a Markov chain on a general state space, with respect to both total variation and Wasserstein distances. For Wasserstein bounds, our main tool is Steinsaltz's convergence theorem for locally contractive random dynamical systems. We describe practical methods for finding Steinsaltz's "drift functions" that prove local contractivity. We then use the idea of "one-shot coupling" to derive criteria that… 

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