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Functional limits of empirical distributions in crossing theory

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  • Lindgren, Georg

Abstract

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.

Suggested Citation

  • Lindgren, Georg, 1977. "Functional limits of empirical distributions in crossing theory," Stochastic Processes and their Applications, Elsevier, vol. 5(2), pages 143-149, May.
    • Handle: RePEc:eee:spapps:v:5:y:1977:i:2:p:143-149
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