Functional limits of empirical distributions in crossing theory

Research output: Contribution to journalArticlepeer-review


We present a functional limit theorem for the empirical level-crossing behaviour of a stationary Gaussian process. This leads to the well-known Slepian model process for a Gaussian process after an upcrossing of a prescribed level as a weak limit in C-space for an empirically defined finite set of functions.We also stress the importance of choosing a suitable topology by giving some natural examples of continuous and non-continuous functionals.
Original languageEnglish
Pages (from-to)143-149
JournalStochastic Processes and their Applications
Issue number2
Publication statusPublished - 1977

Subject classification (UKÄ)

  • Probability Theory and Statistics


  • functional limit theorem
  • empirical process
  • stationary normal process
  • level crossing


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