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Quenched phantom distribution functions for Markov chains

Author

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  • Jakubowski, Adam
  • Truszczyński, Patryk

Abstract

It is known that random walk Metropolis algorithms with heavy-tailed target densities can model atypical (slow) growth of maxima, which in general is exhibited by processes with the extremal index zero. The asymptotics of maxima of such sequences can be analyzed in terms of continuous phantom distribution functions. We show that in a large class of positive Harris recurrent Markov chains (containing the above Metropolis chains) a phantom distribution function can be recovered by starting “at the point” rather than from the stationary distribution.

Suggested Citation

  • Jakubowski, Adam & Truszczyński, Patryk, 2018. "Quenched phantom distribution functions for Markov chains," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 79-83.
    • Handle: RePEc:eee:stapro:v:137:y:2018:i:c:p:79-83
    DOI: 10.1016/j.spl.2018.01.009
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    References listed on IDEAS

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    1. Jakubowski, Adam, 1991. "Relative extremal index of two stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 37(2), pages 281-297, April.
    2. Søren F. Jarner & Gareth O. Roberts, 2007. "Convergence of Heavy‐tailed Monte Carlo Markov Chain Algorithms," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(4), pages 781-815, December.
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