On statistics at level crossings by a stationary process

Statistica Neerlandica

Volumn 56, Issue 2, 2002, Pages 152-164

  Leadbetter, M R ^a   Spaniolo, G V ^a  

^a University of North Carolina at Chapel Hill   (United States)

Author keywords

Marked point process; Palm distribution; Rice's formula; Ship slamming

Indexed keywords

EID: 0036012646     PISSN: 00390402     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9574.00190     Document Type: Article

References (16)

1. Albin, J.M.P. (2000), Extremes and upcrossing intensities for P-differentiable stationary processes, Stochastic Processes and their Applications 87, 199-234.
2. Bulinskaya, E.V. (1961), On the mean number of crossings of a level by a stationary Gaussian process, Theory of Probability and its Applications 6, 435-438.
3. Ito, K. (1964), The expected number of zeros of continuous stationary Gaussian processes, Journal of Mathematics of Kyoto University 3, 207-216.
4. Ivanov, V.A. (1960), On the average number of crossings of a level by sample functions of a stochastic process, Theory of Probability and its Applications 5, 319-323.
5. Kac, M. (1943), On the average number of real roots of a random algebraic equation, Bulletin of the American Mathematical Society 49, 314-320.
6. Kac, M. and D. Slepian (1959), Large excursions of Gaussian processes, Annals of Mathematical Statistics 30, 1215-1228.
7. Kallenberg, O. (1983), Random measures, Academic Press, New York.
8. Leadbetter, M.R. (1966), On crossings of levels and curves by a wide class of stochastic processes, Annals of Mathematical Statistics 37, 260-267.
9. Leadbetter M.R., G. Lindgren, and H. Rootzén (1983), Extremes and related properties of random sequences and processes, Springer, New York.
10. Leadbetter, M.R. and G.V. Spaniolo (2002), Marked crossings by stationary processes and their applications, UNC Statistics Department Center for Stochastic Processes, TR# 526.
11. Ochi, M.K. (1964), Prediction of occurrence and severity of ship slamming at sea, Proceedings 5th Symposium on Naval Hydrodynamics, Bergen, Norway.
12. Rice, S.O. (1944), Mathematical analysis of random noise, Bell System Technical Journal 23, 292-332.
13. Rice, S.O. (1945), Mathematical analysis of random noise, Bell System Technical Journal 24, 46-156.
14. Spaniolo, G.V. (2000), Rice's Formula and Palm Probabilities with applications to structural reliability, Ph.D. Thesis, Statistics Department, UNC-Chapel Hill.
15. Ylvisaker, N.D. (1965), The expected number of zeros of a stationary Gaussian process, Annals of Mathematical Statistics 36, 1043-1046.
16. Zähle, U. (1984), A general Rice formula, Palm measures, and horizontal-window conditioning for random fields, Stochastic Processes and their Applications 17, 265-283.