Hermite polynomial expansion for non-smooth functional of stationary Gaussian processes: Crossings and extremes

Stochastic Processes and their Applications

Volumn 66, Issue 2, 1997, Pages 237-252

  Kratz, Marie F ^a   León, José R ^b  

^a UNIVERSITÉ PARIS DESCARTES   (France)

^b UNIVERSIDAD CENTRAL DE VENEZUELA   (Venezuela)

Author keywords

Crossings; Extremes; Gaussian processes; Hermite polynomial expansion

Indexed keywords

EID: 0031588875     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0304-4149(96)00122-6     Document Type: Article

References (14)

1. M.A. Arcones, Limit theorems for non-linear functional of a stationary Gaussian sequence of vectors. Ann. Probab. 22 (1994) 2242-2274.
2. S. Berman, Sojourn and Extremes of Stochastic Processes (Wadsworth & Brooks-Cole, 1992).
3. E. Cabaña, Estimation of the spectral moment by means of the extrema, Trab. de Estadística y de Invest. operativa 36 (1985) 71-80.
4. D. Chambers and E. Stud, Central limit theorems for nonlinear functionals of stationary Gaussian processes. Probab. Theory Related Fields 80 (1989) 323-346.
5. H. Cramér and M.R. Leadbetter, Stationary and Related Stochastic Processes (Wiley, New York, 1967).
6. D. Geman, On the variance of the number of zeros of a stationary Gaussian process, Ann. Math. Statist. 43 (1972) 977-982.
7. M. Kac, On the average number of real roots of a random algebraic equation. Bull. Amer. Math. Soc. 49 (1943) 314-320.
8. G. Lindgren, Spectral moment estimation by means of level of crossings. Biometrika 61 (1974) 401-418.
9. P. Major, Multiple Wiener-Ito integral, Lecture Notes in Math. 849 (Springer, Berlin, 1981).
10. D. Nualart and M. Wschebor, Intégration par parties dans l'espace de Wiener et approximation du temps local. Probab Theory Relat Fields 90 (1991) 83-109.
11. E. Slud, Multiple Wiener-Itô integral expansions for level-crossing-count functionals, Probab Theory Related Fields 87 (1991) 349-369.
12. E. Slud, MWI expansions for functionals related to level-crossing counts, in: Chaos Expansions, Multiple Wiener-Itô Integrals and their applications by Christian Houdré and Victor Pérez-Abreu, Probability and Stochastics Series (1994a) pp. 125-143.
13. E. Slud, MWI representation of the number of curve-crossings by a differentiable Gaussian process, with applications, Ann. Probab. 22 (1994b) 1355-1380.
14. M. Wschebor, Surfaces Aléatoires, Lecture Notes in Math. No. 1147 (Springer, Berlin, 1985).