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Some properties of the crossings process generated by a stationary χ2 process

Published online by Cambridge University Press:  01 July 2016

Ken Sharpe
Ken Sharpe*
Affiliation:
University of Melbourne
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Abstract

The process generated by the crossings of a fixed level, u, by the process Pn(t) is considered, where

and the Xi(t) are identical, independent, separable, stationary, zero mean, Gaussian processes. A simple formula is obtained for the expected number of upcrossings in a given time interval, sufficient conditions are given for the upcrossings process to tend to a Poisson process as u→∞, and it is shown that under suitable scaling the distribution of the length of an excursion of Pn(t) above u tends to a Rayleigh distribution as u→ ∞.

Keywords

χ2 PROCESSCROSSINGSGAUSSIAN PROCESSPOISSON PROCESSLENGTH OF EXCURSIONSRAYLEIGH DISTRIBUTION
Type
Research Article
Information
Advances in Applied Probability , Volume 10 , Issue 2 , June 1978 , pp. 373 - 391
Copyright
Copyright © Applied Probability Trust 1978 

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