Functional limits of empirical distributions in crossing theory

Georg Lindgren

Stochastic Processes and their Applications, 1977, vol. 5, issue 2, 143-149

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.

Keywords: functional; limit; theorem; empirical; process; stationary; normal; process; level; crossing (search for similar items in EconPapers)
Date: 1977
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