Bounds and asymptotic expansions for the distribution of the Maximum of a smooth stationary Gaussian process
Jean-Marc Azaïs; Christine Cierco-Ayrolles; Alain Croquette
ESAIM: Probability and Statistics (2010)
- Volume: 3, page 107-129
- ISSN: 1292-8100
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topAzaïs, Jean-Marc, Cierco-Ayrolles, Christine, and Croquette, Alain. "Bounds and asymptotic expansions for the distribution of the Maximum of a smooth stationary Gaussian process." ESAIM: Probability and Statistics 3 (2010): 107-129. <http://eudml.org/doc/197730>.
@article{Azaïs2010,
abstract = {
This paper uses the Rice method [18] to give bounds to
the distribution of the maximum of a smooth stationary Gaussian
process. We give simpler expressions of the first two terms of
the Rice series [3,13] for the distribution of the maximum.
Our main contribution is a simpler form of the second factorial moment
of the number of upcrossings which is in some sense a generalization
of Steinberg et al.'s formula
([7] p. 212).
Then, we present a numerical application and asymptotic expansions
that give a new interpretation of a result by
Piterbarg [15].
},
author = {Azaïs, Jean-Marc, Cierco-Ayrolles, Christine, Croquette, Alain},
journal = {ESAIM: Probability and Statistics},
keywords = {Asymptotic expansions; extreme values; stationary Gaussian process;
Rice series; upcrossings.},
language = {eng},
month = {3},
pages = {107-129},
publisher = {EDP Sciences},
title = {Bounds and asymptotic expansions for the distribution of the Maximum of a smooth stationary Gaussian process},
url = {http://eudml.org/doc/197730},
volume = {3},
year = {2010},
}
TY - JOUR
AU - Azaïs, Jean-Marc
AU - Cierco-Ayrolles, Christine
AU - Croquette, Alain
TI - Bounds and asymptotic expansions for the distribution of the Maximum of a smooth stationary Gaussian process
JO - ESAIM: Probability and Statistics
DA - 2010/3//
PB - EDP Sciences
VL - 3
SP - 107
EP - 129
AB -
This paper uses the Rice method [18] to give bounds to
the distribution of the maximum of a smooth stationary Gaussian
process. We give simpler expressions of the first two terms of
the Rice series [3,13] for the distribution of the maximum.
Our main contribution is a simpler form of the second factorial moment
of the number of upcrossings which is in some sense a generalization
of Steinberg et al.'s formula
([7] p. 212).
Then, we present a numerical application and asymptotic expansions
that give a new interpretation of a result by
Piterbarg [15].
LA - eng
KW - Asymptotic expansions; extreme values; stationary Gaussian process;
Rice series; upcrossings.
UR - http://eudml.org/doc/197730
ER -
References
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