Roberts, Gareth O.; Rosenthal, Jeffrey S.; Schwartz, Peter O. Convergence properties of perturbed Markov chains. (English) Zbl 0909.60049 J. Appl. Probab. 35, No. 1, 1-11 (1998). The robustness (stability) of convergence properties of the Markov chain under special perturbations is considered. The perturbations include the case of roundoff error, that occurs naturally in Markov chain Monte Carlo algorithms. Two main results are proved. The first one concerns geometrical ergodicity of the chain. This property is treated in terms of drift condition. It is shown that log-uniform continuity of the drift function ensures the robustness of geometrical ergodicity. The second result shows that the same condition is sufficient for the weak robustness of the stationary distribution of the chain. The total variance stability of the stationary distribution is also considered. Reviewer: E.Kazarovitsky (Kyïv) Cited in 1 ReviewCited in 23 Documents MSC: 60J05 Discrete-time Markov processes on general state spaces 62F99 Parametric inference 62M05 Markov processes: estimation; hidden Markov models Keywords:Markov chain; perturbation; geometric ergodicity; stationary distribution PDFBibTeX XMLCite \textit{G. O. Roberts} et al., J. Appl. Probab. 35, No. 1, 1--11 (1998; Zbl 0909.60049) Full Text: DOI Link