## The Annals of Probability

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

Georg Lindgren

#### 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

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