Abstract
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.
Citation
J. Husler. "Extreme Values and High Boundary Crossings of Locally Stationary Gaussian Processes." Ann. Probab. 18 (3) 1141 - 1158, July, 1990. https://doi.org/10.1214/aop/1176990739
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