## The Annals of Probability

### Occupation Times for Smooth Stationary Processes

#### 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

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