The Annals of Probability

Extreme Values and High Boundary Crossings of Locally Stationary Gaussian Processes

J. Husler

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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.

Article information

Source
Ann. Probab. Volume 18, Number 3 (1990), 1141-1158.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aop/1176990739

Digital Object Identifier
doi:10.1214/aop/1176990739

Mathematical Reviews number (MathSciNet)
MR1062062

JSTOR
links.jstor.org

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 60G15: Gaussian processes

Keywords
Extreme values boundary crossings local stationarity Gaussian processes asymptotic distributions

Citation

Husler, J. Extreme Values and High Boundary Crossings of Locally Stationary Gaussian Processes. Ann. Probab. 18 (1990), no. 3, 1141--1158. doi:10.1214/aop/1176990739. http://projecteuclid.org/euclid.aop/1176990739.


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