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Article Dans Une Revue Probability Surveys Année : 2006

Level crossings and other level functionals of stationary Gaussian processes

Résumé

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.

Dates et versions

hal-00174410 , version 1 (24-09-2007)

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Citer

Marie Kratz. Level crossings and other level functionals of stationary Gaussian processes. Probability Surveys, 2006, 3, pp.230-288. ⟨10.1214/154957806000000087⟩. ⟨hal-00174410⟩
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