Sample Path Properties at Upcrossings

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


Our main concern in the previous chapter has been the numbers and locations of upcrossings of high levels, and the relations between the upcrossings of several adjacent levels.For instance, we know from Theorem 9.3.2 and relation (9.2.3) that for a standard normal process each upcrossing of the high level u = uτ; with a probability p = τ*/τ is accompanied by an upcrossing also of the level
$$u_{\tau * } = u - \frac{{\log p}} {u},$$
asymptotically independently of all other upcrossings of u τ, and uτ*.


Point Process Empirical Distribution Sample Path Sample Function Original Process 
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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