Abstract
We investigate the connections between extremal indices on the one hand and stability of Markov chains on the other hand. Both theories relate to the tail behaviour of stochastic processes, and we find a close link between the extremal index and geometric ergodicity. Our results are illustrated throughout with examples from simple MCMC chains.
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An erratum to this article can be found online at http://dx.doi.org/10.1007/s10687-009-0099-1
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Roberts, G.O., Rosenthal, J.S., Segers, J. et al. Extremal indices, geometric ergodicity of Markov chains, and MCMC. Extremes 9, 213–229 (2006). https://doi.org/10.1007/s10687-006-0028-5
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DOI: https://doi.org/10.1007/s10687-006-0028-5