Level crossings and other level functionals of stationary Gaussian processes
| dc.creator | Kratz, Marie F. | |
| dc.date | 2006-12-20 | |
| dc.date.accessioned | 2026-07-07T07:36:20Z | |
| dc.date.available | 2026-07-07T07:36:20Z | |
| dc.description | This paper presents a synthesis on the mathematical work done on level crossings of stationary Gaussian processes, with some extensions. The main results [(factorial) moments, representation into the Wiener Chaos, asymptotic results, rate of convergence, local time and number of crossings] are described, as well as the different approaches [normal comparison method, Rice method, Stein-Chen method, a general $m$-dependent method] used to obtain them; these methods are also very useful in the general context of Gaussian fields. Finally some extensions [time occupation functionals, number of maxima in an interval, process indexed by a bidimensional set] are proposed, illustrating the generality of the methods. A large inventory of papers and books on the subject ends the survey. | |
| dc.description | Published at http://dx.doi.org/10.1214/154957806000000087 in the Probability Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/math/0612577 | |
| dc.identifier | http://arxiv.org/abs/math/0612577 | |
| dc.identifier | Probability Surveys 2006, Vol. 3, 230-288 | |
| dc.identifier | doi:10.1214/154957806000000087 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/120390 | |
| dc.subject | Probability | |
| dc.subject | 60G15 (Primary) 60G10, 60G12, 60G60, 60G70, 60F05 (Secondary) | |
| dc.title | Level crossings and other level functionals of stationary Gaussian processes | |
| dc.type | text |