Extremal indices, geometric ergodicity of Markov chains, and MCMC

Roberts, Gareth O.;Rosenthal, Jeffrey S.;Segers, Johan;Sousa, Bruno
(2006) Extremes : statistical theory and applications in science, engineering and economics — Vol. 9, n° 3-4, p. 213-229 (2006)

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Authors
  • Roberts, Gareth O.Lancaster University
    Author
  • Rosenthal, Jeffrey S.University of Toronto
    Author
  • Segers, JohanUCLouvain
    Author
  • Sousa, BrunoUniversidade do Minho
    Author
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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Roberts, G. O., Rosenthal, J. S., Segers, J., & Sousa, B. (2006). Extremal indices, geometric ergodicity of Markov chains, and MCMC. Extremes : statistical theory and applications in science, engineering and economics, 9(3-4), 213-229. https://doi.org/10.1007/s10687-006-0028-5 (Original work published 2006)