Slepian models for X2-processes with dependent components with application to envelope upcrossings
- 1 March 1989
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 26 (1) , 36-49
- https://doi.org/10.2307/3214314
Abstract
A Slepian model for the local behaviour near the level upcrossings of a x2-process with dependent Gaussian components is presented. In case of independent components, this model is shown to take on a rather simple form, thereby simplifying earlier results by Aronowich and Adler.The Slepian model is applied to the envelope of a stationary Gaussian process and used to approximate the probability of ‘empty' envelope upcrossings, i.e. the probability that an envelope upcrossing is not followed by a level crossing in the original process.Keywords
This publication has 11 references indexed in Scilit:
- Empty envelope excursions in stationary gaussian processesJournal of Sound and Vibration, 1988
- Extremal Theory for Stochastic ProcessesThe Annals of Probability, 1988
- Extrema and level crossings of χ2 processesAdvances in Applied Probability, 1986
- Behaviour of χ2 processes at extremaAdvances in Applied Probability, 1985
- Extreme values and crossings for theX2-Process and Other Functions of Multidimensional Gaussian Processes, by Reliability ApplicationsAdvances in Applied Probability, 1980
- Model Processes in Nonlinear Prediction with Application to Detection and AlarmThe Annals of Probability, 1980
- Point processes of exits by bivariate Gaussian processes and extremal theory for the χ2-process and its concomitantsJournal of Multivariate Analysis, 1980
- Some properties of the crossings process generated by a stationary χ2 processAdvances in Applied Probability, 1978
- On the Distribution of the First-Passage Time for Normal Stationary Random ProcessesJournal of Applied Mechanics, 1975
- Large Excursions of Gaussian ProcessesThe Annals of Mathematical Statistics, 1959