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Extremes of Continuous Parameter Stationary Processes

  • M. R. Leadbetter
  • Georg Lindgren
  • Holger Rootzén
Part of the Springer Series in Statistics book series (SSS)

Abstract

Our primary task in this chapter will be to discuss continuous parameter analogues of the sequence results of Chapter 3, and, in particular, to obtain a corresponding version of the Extremal Types Theorem which applies in the continuous parameter case. This will be taken up in the first section, using a continuous parameter analogue of the dependence restriction D(un). Limits for probabilities P{M(T) ≤ uT} are then considered for arbitrary families of constants {uT}, leading, in particular, to a determination of domains of attraction.

Keywords

Poisson Process Point Process Asymptotic Distribution Continuous Parameter Parameter Context 
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

© Springer-Verlag New York Inc. 1983

Authors and Affiliations

  • M. R. Leadbetter
    • 1
  • Georg Lindgren
    • 2
  • Holger Rootzén
    • 3
  1. 1.Department of StatisticsThe University of North CarolinaChapel HillUSA
  2. 2.Department of Mathematical StatisticsUniversity of LundLundSweden
  3. 3.Institute of Mathematical StatisticsUniversity of CopenhagenCopenhagen øDenmark

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