On the tails of the distribution of the maximum of a smooth stationary Gaussian process
Jean-Marc Azaïs; Jean-Marc Bardet; Mario Wschebor
ESAIM: Probability and Statistics (2010)
- Volume: 6, page 177-184
- ISSN: 1292-8100
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topAzaïs, Jean-Marc, Bardet, Jean-Marc, and Wschebor, Mario. "On the tails of the distribution of the maximum of a smooth stationary Gaussian process." ESAIM: Probability and Statistics 6 (2010): 177-184. <http://eudml.org/doc/104286>.
@article{Azaïs2010,
abstract = {
We study the tails of the distribution of the maximum of a stationary
Gaussian process on a bounded interval of the real line. Under regularity
conditions including the existence of the spectral moment of order 8,
we give an additional term for this asymptotics. This widens the
application of an expansion given originally by Piterbarg [CITE] for
a sufficiently small interval.
},
author = {Azaïs, Jean-Marc, Bardet, Jean-Marc, Wschebor, Mario},
journal = {ESAIM: Probability and Statistics},
keywords = {Tail of distribution of the maximum; stationary Gaussian
processes.; stationary Gaussian processes; distribution of maximum; spectral moment},
language = {eng},
month = {3},
pages = {177-184},
publisher = {EDP Sciences},
title = {On the tails of the distribution of the maximum of a smooth stationary Gaussian process},
url = {http://eudml.org/doc/104286},
volume = {6},
year = {2010},
}
TY - JOUR
AU - Azaïs, Jean-Marc
AU - Bardet, Jean-Marc
AU - Wschebor, Mario
TI - On the tails of the distribution of the maximum of a smooth stationary Gaussian process
JO - ESAIM: Probability and Statistics
DA - 2010/3//
PB - EDP Sciences
VL - 6
SP - 177
EP - 184
AB -
We study the tails of the distribution of the maximum of a stationary
Gaussian process on a bounded interval of the real line. Under regularity
conditions including the existence of the spectral moment of order 8,
we give an additional term for this asymptotics. This widens the
application of an expansion given originally by Piterbarg [CITE] for
a sufficiently small interval.
LA - eng
KW - Tail of distribution of the maximum; stationary Gaussian
processes.; stationary Gaussian processes; distribution of maximum; spectral moment
UR - http://eudml.org/doc/104286
ER -
References
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- 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.
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- 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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