Occupation Times for Smooth Stationary Processes

• DOI: 10.1214/aop/1176997029
• Publication Date: 2007-12-17T16:28:29Z
• Authors: D. Geman; J. Horowitz
• Keywords: Absolute continuity; Stationary process

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