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Max-Stable Processes

Extremes and Environmental Risk

  1. Simone A. Padoan

Published Online: 15 JAN 2013

DOI: 10.1002/9780470057339.vnn022

Encyclopedia of Environmetrics

Encyclopedia of Environmetrics

How to Cite

Padoan, S. A. 2013. Max-Stable Processes. Encyclopedia of Environmetrics. 4.

Author Information

  1. University of Padua, Padua, Italy

Publication History

  1. Published Online: 15 JAN 2013


Environmental problems such as floods require statistical analysis that takes into account the complex nature of the data, namely, the observations that are sampled at different spatial points in a given region for a certain time. Thus the spatial dependence structure cannot be ignored. Extreme statistics for the design of structures for flood protection, for the study of the structural failures such as those in bridges, dams, and so on, for the prediction of heat waves, and other spatial extremes should be based on a solid theoretical framework. Max-stable processes provide such a theory and in the last decade have emerged as fertile ground for research and have become a common tool for the statistical modeling of spatial extremes. This article provides a summary of max-stable processes.


  • Brown–Resnick processes;
  • coefficient of tail dependence;
  • ergodicity;
  • extremes;
  • extremal coefficient function;
  • Fréchet distributions;
  • Gaussian processes;
  • Gumbel distributions;
  • Hüsler–Reiss model;
  • mixing;
  • multivariate extremes;
  • pointwise maximum;
  • Poisson point processes;
  • stationary max-stable processes