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Zbl 1092.60027
Mitrophanov, A.Yu.
Sensitivity and convergence of uniformly ergodic Markov chains. (English)
[J] J. Appl. Probab. 42, No. 4, 1003-1014 (2005). ISSN 0021-9002

Summary: For uniformly ergodic Markov chains, we obtain new perturbation bounds which relate the sensitivity of the chain under perturbation to its rate of convergence to stationarity. In particular, we derive sensitivity bounds in terms of the ergodicity coefficient of the iterated transition kernel, which improve upon the bounds obtained by other authors. We discuss convergence bounds that hold in the case of finite state space, and consider numerical examples to compare the accuracy of different perturbation bounds.

MSC 2000:: *60J05 Markov processes with discrete parameter
60J10 Markov chains with discrete parameter
60J35 Transition functions

Keywords: uniform ergodicity; rate of convergence; ergodicity coefficient; perturbation bound; sensitivity analysis

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