We consider the large values of a locally stationary Gaussian process which satisfies Berman's condition on the long range dependence. The paper presents some limit results on the exceedances of the process above a certain general smooth high boundary. This allows deriving the limiting distribution of the maximum up to time $T$, for example, in the case of a standardized process with a constant boundary or in the case of a nonstandardized process with a smooth trend.
Publié le : 1990-07-14
Classification:
Extreme values,
boundary crossings,
local stationarity,
Gaussian processes,
asymptotic distributions,
60F05,
60G15
@article{1176990739,
author = {Husler, J.},
title = {Extreme Values and High Boundary Crossings of Locally Stationary Gaussian Processes},
journal = {Ann. Probab.},
volume = {18},
number = {4},
year = {1990},
pages = { 1141-1158},
language = {en},
url = {http://dml.mathdoc.fr/item/1176990739}
}
Husler, J. Extreme Values and High Boundary Crossings of Locally Stationary Gaussian Processes. Ann. Probab., Tome 18 (1990) no. 4, pp. 1141-1158. http://gdmltest.u-ga.fr/item/1176990739/