## The Annals of Probability

### Extreme Values and High Boundary Crossings of Locally Stationary Gaussian Processes

J. Husler

#### 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

http://projecteuclid.org/euclid.aop/1176990739

Digital Object Identifier
doi:10.1214/aop/1176990739

Mathematical Reviews number (MathSciNet)
MR1062062

JSTOR