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.
Original language | English |
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Pages (from-to) | 143-149 |
Journal | Stochastic Processes and their Applications |
Volume | 5 |
Issue number | 2 |
Publication status | Published - 1977 |
Subject classification (UKÄ)
- Probability Theory and Statistics
Free keywords
- functional limit theorem
- empirical process
- stationary normal process
- level crossing