Occupation Times for Smooth Stationary Processes
Geman, D. ; Horowitz, J.
Ann. Probab., Tome 1 (1973) no. 5, p. 131-137 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
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.
Publié le : 1973-02-14
Classification:  Occupation-time density,  stationary process,  level crossings,  60G10,  60G17,  60G15 
@article{1176997029,
     author = {Geman, D. and Horowitz, J.},
     title = {Occupation Times for Smooth Stationary Processes},
     journal = {Ann. Probab.},
     volume = {1},
     number = {5},
     year = {1973},
     pages = { 131-137},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176997029}
}

Geman, D.; Horowitz, J. Occupation Times for Smooth Stationary Processes. Ann. Probab., Tome 1 (1973) no. 5, pp.  131-137. http://gdmltest.u-ga.fr/item/1176997029/