Capacities, Large Deviations and Loglog Laws

  • George L. O’brien
  • Wim Vervaat
Part of the Progress in Probabilty book series (PRPR, volume 25)


Spaces of capacities are considered with their natural subspaces and two topologies, the vague and the narrow. Large deviation principles are identified as a class of limit relations of capacities. Narrow large deviation principles occasionally can be tied to loglog laws, and this relationship is studied. Specific narrow large deviation principles and loglog laws are presented (without proof) for the Poisson process on the positive quadrant that is the natural foundation for extremal processes and spectrally positive stable motions. Related loglog laws for extremal processes and stable motions are discussed.


Radon Measure Iterate Logarithm Large Deviation Principle Stable Motion General Topological Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Birkhäuser Boston 1991

Authors and Affiliations

  • George L. O’brien
    • 1
  • Wim Vervaat
    • 2
  1. 1.Department of MathematicsYork UniversityNorth YorkCanada
  2. 2.Mathematisch InstituutKatholieke UniversiteitNijmegenThe Netherlands

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