The Annals of Probability

Occupation Times for Smooth Stationary Processes

D. Geman and J. Horowitz

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Abstract

An occupation-time density is identified for a class of absolutely continuous functions $x(t)$ in terms of $x'(t)$ and the number of times that $x(t)$ assumes the values in its range. This result is applied to stationary random processes with a finite second spectral moment. As a by-product, a generalization of Rice's formula for the mean number of crossings is obtained.

Article information

Source
Ann. Probab. Volume 1, Number 1 (1973), 131-137.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176997029

Digital Object Identifier
doi:10.1214/aop/1176997029

Mathematical Reviews number (MathSciNet)
MR350833

Zentralblatt MATH identifier
0264.60027

JSTOR
links.jstor.org

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

Keywords
Occupation-time density stationary process level crossings

Citation

Geman, D.; Horowitz, J. Occupation Times for Smooth Stationary Processes. Ann. Probab. 1 (1973), no. 1, 131--137. doi:10.1214/aop/1176997029. https://projecteuclid.org/euclid.aop/1176997029


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