Open Access
February, 1973 Occupation Times for Smooth Stationary Processes
D. Geman, J. Horowitz
Ann. Probab. 1(1): 131-137 (February, 1973). DOI: 10.1214/aop/1176997029


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.


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D. Geman. J. Horowitz. "Occupation Times for Smooth Stationary Processes." Ann. Probab. 1 (1) 131 - 137, February, 1973.


Published: February, 1973
First available in Project Euclid: 19 April 2007

zbMATH: 0264.60027
MathSciNet: MR350833
Digital Object Identifier: 10.1214/aop/1176997029

Primary: 60G10
Secondary: 60G15 , 60G17

Keywords: level crossings , Occupation-time density , stationary process

Rights: Copyright © 1973 Institute of Mathematical Statistics

Vol.1 • No. 1 • February, 1973
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