Limit distribution of the last exit time for stationary random sequences

  • Jürg Hüsler
Article
  • 35 Downloads

Summary

For a strictly stationary random sequence (Xi)i≧0 we find sufficient conditions such that the distribution of the last exit time tβ = max{iXi>βi} (β>0) tends weakly to a nondegenerate limit distribution as β↓0.

Keywords

Stochastic Process Probability Theory Mathematical Biology Random Sequence Limit Distribution 

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References

  1. 1.
    Hüsler, J.: On limit distributions of first crossing points of Gaussian sequences. Stochastic Processes Appl. 6, 65–75 (1977)Google Scholar
  2. 2.
    Hüsler, J.: The limiting behaviour of the last exit time for sequences of independent, identically distributed random variables. Z. Wahrscheinlichkeitstheorie verw. Gebiete 50, 159–164 (1979)Google Scholar
  3. 3.
    Hüsler, J.: Hinreichende Bedingungen für die Gültigkeit einer Grenzverteilung der letzten Austrittszeit bei Gaussfolgen. Techn. Berichte No. 2, Institut f. math. Statistik, Universität Bern, 1980Google Scholar
  4. 4.
    Leadbetter, M.R.: On extreme values in stationary sequences. Z. Wahrscheinlichkeitstheorie verw. Gebiete 28, 289–303 (1974)Google Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • Jürg Hüsler
    • 1
  1. 1.Department of math. StatisticsUniversity of BerneBernSwitzerland

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