# Geometric convergence bounds for Markov chains in Wasserstein distance based on generalized drift and contraction conditions

@article{Qin2019GeometricCB, title={Geometric convergence bounds for Markov chains in Wasserstein distance based on generalized drift and contraction conditions}, author={Qian Qin and J. Hobert}, journal={arXiv: Probability}, year={2019} }

Let $\{X_n\}_{n=0}^\infty$ denote an ergodic Markov chain on a general state space that has stationary distribution $\pi$. This article concerns upper bounds on the $L_1$-Wasserstein distance between the distribution of $X_n$ and $\pi$ in the case where the underlying metric is potentially unbounded. In particular, an explicit geometric bound on the distance to stationarity is derived using generalized drift and contraction conditions whose parameters vary across the state space. A corollary of… Expand

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