Sensitivity and convergence of uniformly ergodic Markov chains

2005/12/01 by A. Yu. Mitrophanov, Alexander Y. Mitrophanov · 7 citations
Mathematics · Biochemistry, Genetics and Molecular Biology · #Markov Chains and Monte Carlo Methods #Stochastic processes and statistical mechanics #Protein Structure and Dynamics

paper · doi:10.1239/jap/1134587812

Abstract

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.

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