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Geophysical Monograph Series



  • extreme events
  • long-range dependence
  • stochastic processes
  • records
  • persistent alpha stable
  • solar influx

Index Terms

  • 0560 Computational Geophysics: Numerical solutions
  • 3225 Mathematical Geophysics: Numerical approximations and analysis
  • 3265 Mathematical Geophysics: Stochastic processes
  • 3270 Mathematical Geophysics: Time series analysis



Extreme Value and Record Statistics in Heavy-Tailed Processes With Long-Range Memory

A. Y. Schumann, N. R. Moloney, and J. Davidsen

Extreme events are an important theme in various areas of science because of their typically devastating effects on society and their scientific complexities. The latter is particularly true if the underlying dynamics does not lead to independent extreme events as often observed in natural systems. Here we focus on this case and consider stationary stochastic processes that are characterized by long-range memory and heavy-tailed distributions, often called fractional Lévy noise. While the size distribution of extreme events is not affected by the long-range memory in the asymptotic limit and remains a Fréchet distribution, there are strong finite-size effects if the memory leads to persistence in the underlying dynamics. Moreover, we show that this persistence is also present in the extreme events, which allows one to make a time-dependent hazard assessment of future extreme events based on events observed in the past. This has direct applications in the field of space weather as we discuss specifically for the case of the solar power influx into the magnetosphere. Finally, we show how the statistics of records, or record-breaking extreme events, is affected by the presence of long-range memory.

Citation: Schumann, A. Y., N. R. Moloney, and J. Davidsen (2012), Extreme value and record statistics in heavy-tailed processes with long-range memory, in Extreme Events and Natural Hazards: The Complexity Perspective, Geophys. Monogr. Ser., vol. 196, edited by A. S. Sharma et al. 315–334, AGU, Washington, D. C., doi:10.1029/2011GM001088.

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