The Annals of Probability

A Note on the Asymptotic Independence of High Level Crossings for Dependent Gaussian Processes

Georg Lindgren

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Abstract

It is shown that the numbers of high level crossings by $p$ dependent stationary Gaussian processes have asymptotically independent Poisson distributions if the observation interval and the height of the level increase in a coordinated way. The processes may be highly correlated, even linearly dependent.

Article information

Source
Ann. Probab., Volume 2, Number 3 (1974), 535-539.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176996672

Digital Object Identifier
doi:10.1214/aop/1176996672

Mathematical Reviews number (MathSciNet)
MR372977

Zentralblatt MATH identifier
0288.60038

JSTOR
links.jstor.org

Subjects
Primary: 60G15: Gaussian processes
Secondary: 60G10: Stationary processes 60G17: Sample path properties

Keywords
level crossings stationary Gaussian processes cross-correlation function

Citation

Lindgren, Georg. A Note on the Asymptotic Independence of High Level Crossings for Dependent Gaussian Processes. Ann. Probab. 2 (1974), no. 3, 535--539. doi:10.1214/aop/1176996672. https://projecteuclid.org/euclid.aop/1176996672


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