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Extremes of Random Sequences

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Laws of Small Numbers: Extremes and Rare Events

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Abstract

We develop the general theory of extremes and exceedances of high boundaries by non-stationary random sequences. Of main interest is the asymptotic convergence of the point processes of exceedances or of clusters of exceedances. These results are then applied for special cases, as stationary, independent and particular nonstationary random sequences.

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Authors and Affiliations

  1. Institute of Mathematics, University of Würzburg, Am Hubland, 97074, Würzburg, Germany

    Michael Falk

  2. Department of Mathematical Statistics and Actuarial Science, University of Berne, Sidlerstrasse 5, 3012, Bern, Switzerland

    Jürg Hüsler

  3. Department of Mathematics, University of Siegen, Walter Flex Str. 3, 57068, Siegen, Germany

    Rolf-Dieter Reiss

Authors
  1. Michael Falk
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  2. Jürg Hüsler
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  3. Rolf-Dieter Reiss
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Correspondence to Michael Falk .

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Falk, M., Hüsler, J., Reiss, RD. (2011). Extremes of Random Sequences. In: Laws of Small Numbers: Extremes and Rare Events. Springer, Basel. https://doi.org/10.1007/978-3-0348-0009-9_9

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