Roberts, Gareth O.; Rosenthal, Jeffrey S. Shift-coupling and convergence rates of ergodic averages. (English) Zbl 0871.60046 Commun. Stat., Stochastic Models 13, No. 1, 147-165 (1997). Summary: We study convergence of Markov chains \(\{X_k\}\) to their stationary distributions \(\pi(\cdot)\). Much recent work has used coupling to get quantitative bounds on the total variation distance between the law \({\mathcal L}(X_n)\) and \(\pi(\cdot)\). We use shift-coupling to get quantitative bounds on the total variation distance between the ergodic average law \(\frac 1n \sum^n_{k=1}{\mathcal L}(X_k)\) and \(\pi(\cdot)\). This avoids certain problems, related to periodicity and near-periodicity of the Markov chain, which have plagued previous work. Cited in 11 Documents MSC: 60J10 Markov chains (discrete-time Markov processes on discrete state spaces) 60F05 Central limit and other weak theorems Keywords:shift-coupling; computable bounds; Markov chain Monte Carlo; drift condition; minorization condition; small set PDFBibTeX XMLCite \textit{G. O. Roberts} and \textit{J. S. Rosenthal}, Commun. Stat., Stochastic Models 13, No. 1, 147--165 (1997; Zbl 0871.60046) Full Text: DOI