We introduce a general method, which combines the one developed by the authors in 1997 and one derived from the work of Malevich (1969), Cuzick (1976) and mainly Berman (1992), to provide in an easy way a CLT for level functionals of a Gaussian process, as well as a CLT for the length of a level curve of a Gaussian field.
Publié le : 2001-07-05
Classification:
asymptotic variance,
central limit theorem,
crossings,
Gaussian fields,
Gaussian processes,
Hermite polynomials,
level curve,
maxima,
sojourn time,
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR],
[MATH.MATH-ST]Mathematics [math]/Statistics [math.ST],
[STAT.TH]Statistics [stat]/Statistics Theory [stat.TH]
@article{hal-00171272,
author = {Kratz, Marie and Leon, J. R.},
title = {Central limit theorems for level's functionals of stationary Gaussian processes and fields},
journal = {HAL},
volume = {2001},
number = {0},
year = {2001},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00171272}
}
Kratz, Marie; Leon, J. R. Central limit theorems for level's functionals of stationary Gaussian processes and fields. HAL, Tome 2001 (2001) no. 0, . http://gdmltest.u-ga.fr/item/hal-00171272/