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1 results

  • Functionals of clusters of extremes

  • Part of
  • Johan Segers
  • Journal:
    Advances in Applied Probability / Volume 35 / Issue 4 / December 2003
    Published online by Cambridge University Press:
    01 July 2016, pp. 1028-1045
    Print publication:
    December 2003

  • For arbitrary stationary sequences of random variables satisfying a mild mixing condition, distributional approximations are established for functionals of clusters of exceedances over a high threshold. The approximations are in terms of the distribution of the process conditionally on the event that the first variable exceeds the threshold. This conditional distribution is shown to converge to a nontrivial limit if the finite-dimensional distributions of the process are in the domain of attraction of a multivariate extreme-value distribution. In this case, therefore, limit distributions are obtained for functionals of clusters of extremes, thereby generalizing results for higher-order stationary Markov chains by Yun (2000).