×

Shift-coupling and convergence rates of ergodic averages. (English) Zbl 0871.60046

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.

MSC:

60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
60F05 Central limit and other weak theorems
PDFBibTeX XMLCite
Full Text: DOI