On the tails of the distribution of the maximum of a smooth stationary Gaussian process

Free access article

Issue		ESAIM: PS Volume 6, 2002


Page(s)		177 - 184
DOI		10.1051/ps:2002010

References

M. Abramowitz and I.A. Stegun, Handbook of Mathematical functions with Formulas, graphs and mathematical Tables. Dover, New-York (1972).
R.J. Adler, An introduction to Continuity, Extrema and Related Topics for General Gaussian Processes. IMS, Hayward, CA (1990).
J.-M. Azaïs and J.-M. Bardet, Unpublished manuscript (2000).
J.-M. Azaïs and C. Cierco-Ayrolles, An asymptotic test for quantitative gene detection. Ann. Inst. H. Poincaré Probab. Statist. (to appear).
J.-M. Azaïs, C. Cierco-Ayrolles and A. Croquette, Bounds and asymptotic expansions for the distribution of the maximum of a smooth stationary Gaussian process. ESAIM: P&S 3 (1999) 107-129.
J.-M. Azaïs and M. Wschebor, The Distribution of the Maximum of a Gaussian Process: Rice Method Revisited, in In and out of equilibrium: Probability with a physical flavour. Birkhauser, Coll. Progress in Probability (2002) 321-348.
H. Cramér and M.R. Leadbetter, Stationary and Related Stochastic Processes. J. Wiley & Sons, New-York (1967).
R.B. Davies, Hypothesis testing when a nuisance parameter is present only under the alternative. Biometrika 64 (1977) 247-254.
J. Dieudonné, Calcul Infinitésimal. Hermann, Paris (1980).
R.N. Miroshin, Rice series in the theory of random functions. Vestn. Leningrad Univ. Math. 1 (1974) 143-155.
V.I. Piterbarg, Comparison of distribution functions of maxima of Gaussian processes. Theoret. Probab. Appl. 26 (1981) 687-705.

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